Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer from the following (any seven):
Air is compressed adiabatically in a steady flow process with negligible change in potential and kinetic energy. The work done in the process is given by
Which one of the following is the extensive property of a thermodynamic system?
The time constant of a thermocouple is the time taken to attain
For the expression $ \int pdv $ to represent the work, which of the following conditions should apply?
For a closed system, the difference between the heat added to the system and the work done by the system is equal to the change in
Change in internal energy in a reversible process occurring in a closed system is equal to the heat transferred, if the process occurs at constant
A reversible engine operates between temperatures 900 K and $ T_2 $ ($ T_2 < 900 \text{ K} $), and another reversible engine between $ T_2 $ and 400 K ($ T_2> 400 \text{ K} $) in series. What is the value of $ T_2 $ if work outputs of both the engines are equal?
A Carnot engine operates between $ 327^\circ\text{C} $ and $ 27^\circ\text{C} $. If the engine produces 300 kJ of work, what is the entropy change during heat addition?
In which one of the following situations the entropy change will be negative?
Neglecting changes in kinetic energy and potential energy, for unit mass the availability in a non-flow process becomes $ a = \phi - \phi_0 $, where $ \phi $ is the availability function of the
Q.2 Solve both questions :
Define thermodynamic equilibrium. With the help of practical example, explain the phenomenon of achieving a thermodynamic equilibrium of system.
0.1 $ \text{m}^3 $ of an ideal gas at 300 K and 1 bar is compressed adiabatically to 8 bars. It is then cooled at constant volume and expanded isothermally so as to reach the condition from where it started. Calculate (i) pressure at the end of constant volume cooling, (ii) change in internal energy during constant volume process and (iii) net work done and heat transferred during the cycle.
Q.3 Solve both questions :
What is SFEE? Derive the SFEE equation of an open system.
Air at a temperature of $ 20^\circ\text{C} $ passes through a heat exchanger at a velocity of 40 m/s where its temperature is raised to $ 820^\circ\text{C} $. It then enters a turbine with same velocity of 40 m/s and expands till the temperature falls to $ 620^\circ\text{C} $. On leaving the turbine, the air is taken at a velocity of 55 m/s to a nozzle where it expands until the temperature has fallen to $ 510^\circ\text{C} $. If the air flow rate is 2.5 kg/s calculate (i) rate of heat transfer to the air in the heat exchanger, (ii) the power output from the turbine assuming no heat loss, (iii) the velocity at exit from the nozzle, assuming no heat loss. Take the enthalpy of air as $ h = C_pt $, where $ C_p $ is the specific heat equal to 1.005 kJ/kg$^\circ\text{C}$ and $ t $ be the temperature.
Q.4 Solve both questions :
Draw a neat sketch of throttling calorimeter and explain how dryness fraction of steam is determined. Clearly explain its limitations.
A quantity of steam at 13 bars and 0.8 dryness occupies 0.1 $ \text{m}^3 $. Determine the heat supplied to raise the temperature of the steam to $ 250^\circ\text{C} $ at constant pressure and percentage of this heat which appears as external work. Take specific heat for superheated steam as 2.2 kJ/kgK.
Q.5 Solve both questions :
Prove the equivalence of Clausius statement to the Kelvin-Planck statement with schematic diagram.
A reversible heat pump is used to maintain a temperature of $ 0^\circ\text{C} $ in a refrigerator when it rejects the heat to the surroundings at $ 25^\circ\text{C} $. (i) If the heat removal rate from the refrigerator is 1440 kJ/min, determine the COP of the machine and work input required. (ii) If the required input to run the pump is developed by a reversible engine which receives heat at $ 380^\circ\text{C} $ and rejects heat to atmosphere, then determine the overall COP of the system.
Q.6 Solve both questions :
Derive expressions for entropy changes for a closed system in the cases- (i) general case for change of entropy of a gas, (ii) heating a gas at constant volume and (iii) heating a gas at constant pressure.
1.2 $ \text{m}^3 $ of air is heated reversibly at constant pressure from 300 K to 600 K, and is then cooled reversibly at constant volume back to initial temperature. If the initial pressure is 1 bar, calculate (i) the net heat flow, (ii) the overall change in entropy. Represent the processes on T-S plot.
Q.7 Solve both questions :
Deduce an expression for decrease in available energy when heat is transferred through a finite temperature difference.
8 kg of air at 650 K and 5.5 bars pressure is enclosed in a closed system. If the atmospheric temperature and pressure are 300 K and 1 bar respectively, determine (i) the availability if the system goes through the ideal work producing process, (ii) the availability and effectiveness if the air is cooled at constant pressure to atmospheric temperature without bringing it to complete dead state. Take $ C_v = 0.718 \text{ kJ/kgK} $; $ C_p = 1.005 \text{ kJ/kgK} $.
Q.8 Solve both questions :
A mass of air initially at $ 260^\circ\text{C} $ and a pressure of 6.86 bars has a volume of 0.03 $ \text{m}^3 $. The air is expanded at constant pressure to 0.09 $ \text{m}^3 $ a polytropic process with $ n = 1.5 $ is then carried out, followed by a constant temperature process which completes the cycle. All processes are reversible. Find (i) the heat received and rejected in the cycle, (ii) the efficiency of the cycle. Show the cycle on p-v and T-s planes.
A steel flask of 0.04 $ \text{m}^3 $ capacity is to be used to store nitrogen at 120 bars, $ 20^\circ\text{C} $. The flask is to be protected against excessive pressure by a fusible plug which will melt and allow the gas to escape if the temperature rises too high. (i) How many kg of nitrogen will the flask hold at the designed conditions? (ii) At what temperature must the fusible plug melt in order to limit the pressure of a full flask to a maximum of 150 bars?
Q.9 Solve both questions :
Define the following: (i) Dew-point temperature (ii) Relative humidity (iii) Degree of saturation
On a particular day, the atmospheric air was found to have a dry bulb temperature of $ 30^\circ\text{C} $ and a wet bulb temperature of $ 18^\circ\text{C} $. The barometric pressure was observed to be 756 mm of Hg. Using the tables of psychrometric properties of air, determine the relative humidity, the specific humidity, the dew-point temperature, the enthalpy of air per kg of dry air and the volume of mixture per kg of dry air.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer from the following (any seven):
Air is compressed adiabatically in a steady flow process with negligible change in potential and kinetic energy. The work done in the process is given by
Which one of the following is the extensive property of a thermodynamic system?
The time constant of a thermocouple is the time taken to attain
For the expression $ \int pdv $ to represent the work, which of the following conditions should apply?
For a closed system, the difference between the heat added to the system and the work done by the system is equal to the change in
Change in internal energy in a reversible process occurring in a closed system is equal to the heat transferred, if the process occurs at constant
A reversible engine operates between temperatures 900 K and $ T_2 $ ($ T_2 < 900 \text{ K} $), and another reversible engine between $ T_2 $ and 400 K ($ T_2> 400 \text{ K} $) in series. What is the value of $ T_2 $ if work outputs of both the engines are equal?
A Carnot engine operates between $ 327^\circ\text{C} $ and $ 27^\circ\text{C} $. If the engine produces 300 kJ of work, what is the entropy change during heat addition?
In which one of the following situations the entropy change will be negative?
Neglecting changes in kinetic energy and potential energy, for unit mass the availability in a non-flow process becomes $ a = \phi - \phi_0 $, where $ \phi $ is the availability function of the
Q.2 Solve both questions :
Define thermodynamic equilibrium. With the help of practical example, explain the phenomenon of achieving a thermodynamic equilibrium of system.
0.1 $ \text{m}^3 $ of an ideal gas at 300 K and 1 bar is compressed adiabatically to 8 bars. It is then cooled at constant volume and expanded isothermally so as to reach the condition from where it started. Calculate (i) pressure at the end of constant volume cooling, (ii) change in internal energy during constant volume process and (iii) net work done and heat transferred during the cycle.
Q.3 Solve both questions :
What is SFEE? Derive the SFEE equation of an open system.
Air at a temperature of $ 20^\circ\text{C} $ passes through a heat exchanger at a velocity of 40 m/s where its temperature is raised to $ 820^\circ\text{C} $. It then enters a turbine with same velocity of 40 m/s and expands till the temperature falls to $ 620^\circ\text{C} $. On leaving the turbine, the air is taken at a velocity of 55 m/s to a nozzle where it expands until the temperature has fallen to $ 510^\circ\text{C} $. If the air flow rate is 2.5 kg/s calculate (i) rate of heat transfer to the air in the heat exchanger, (ii) the power output from the turbine assuming no heat loss, (iii) the velocity at exit from the nozzle, assuming no heat loss. Take the enthalpy of air as $ h = C_pt $, where $ C_p $ is the specific heat equal to 1.005 kJ/kg$^\circ\text{C}$ and $ t $ be the temperature.
Q.4 Solve both questions :
Draw a neat sketch of throttling calorimeter and explain how dryness fraction of steam is determined. Clearly explain its limitations.
A quantity of steam at 13 bars and 0.8 dryness occupies 0.1 $ \text{m}^3 $. Determine the heat supplied to raise the temperature of the steam to $ 250^\circ\text{C} $ at constant pressure and percentage of this heat which appears as external work. Take specific heat for superheated steam as 2.2 kJ/kgK.
Q.5 Solve both questions :
Prove the equivalence of Clausius statement to the Kelvin-Planck statement with schematic diagram.
A reversible heat pump is used to maintain a temperature of $ 0^\circ\text{C} $ in a refrigerator when it rejects the heat to the surroundings at $ 25^\circ\text{C} $. (i) If the heat removal rate from the refrigerator is 1440 kJ/min, determine the COP of the machine and work input required. (ii) If the required input to run the pump is developed by a reversible engine which receives heat at $ 380^\circ\text{C} $ and rejects heat to atmosphere, then determine the overall COP of the system.
Q.6 Solve both questions :
Derive expressions for entropy changes for a closed system in the cases- (i) general case for change of entropy of a gas, (ii) heating a gas at constant volume and (iii) heating a gas at constant pressure.
1.2 $ \text{m}^3 $ of air is heated reversibly at constant pressure from 300 K to 600 K, and is then cooled reversibly at constant volume back to initial temperature. If the initial pressure is 1 bar, calculate (i) the net heat flow, (ii) the overall change in entropy. Represent the processes on T-S plot.
Q.7 Solve both questions :
Deduce an expression for decrease in available energy when heat is transferred through a finite temperature difference.
8 kg of air at 650 K and 5.5 bars pressure is enclosed in a closed system. If the atmospheric temperature and pressure are 300 K and 1 bar respectively, determine (i) the availability if the system goes through the ideal work producing process, (ii) the availability and effectiveness if the air is cooled at constant pressure to atmospheric temperature without bringing it to complete dead state. Take $ C_v = 0.718 \text{ kJ/kgK} $; $ C_p = 1.005 \text{ kJ/kgK} $.
Q.8 Solve both questions :
A mass of air initially at $ 260^\circ\text{C} $ and a pressure of 6.86 bars has a volume of 0.03 $ \text{m}^3 $. The air is expanded at constant pressure to 0.09 $ \text{m}^3 $ a polytropic process with $ n = 1.5 $ is then carried out, followed by a constant temperature process which completes the cycle. All processes are reversible. Find (i) the heat received and rejected in the cycle, (ii) the efficiency of the cycle. Show the cycle on p-v and T-s planes.
A steel flask of 0.04 $ \text{m}^3 $ capacity is to be used to store nitrogen at 120 bars, $ 20^\circ\text{C} $. The flask is to be protected against excessive pressure by a fusible plug which will melt and allow the gas to escape if the temperature rises too high. (i) How many kg of nitrogen will the flask hold at the designed conditions? (ii) At what temperature must the fusible plug melt in order to limit the pressure of a full flask to a maximum of 150 bars?
Q.9 Solve both questions :
Define the following: (i) Dew-point temperature (ii) Relative humidity (iii) Degree of saturation
On a particular day, the atmospheric air was found to have a dry bulb temperature of $ 30^\circ\text{C} $ and a wet bulb temperature of $ 18^\circ\text{C} $. The barometric pressure was observed to be 756 mm of Hg. Using the tables of psychrometric properties of air, determine the relative humidity, the specific humidity, the dew-point temperature, the enthalpy of air per kg of dry air and the volume of mixture per kg of dry air.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer from the following (any seven):
For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is
Ice kept in a well insulated thermoflask is an example of which system?
Pressure reaches a value of absolute zero
Work done in a free expansion process is
Two blocks which are at different states are brought into contact with each other and allowed to reach a final state of thermal equilibrium. The final temperature attained is specified by the
A gas is compressed in a cylinder by a movable piston to a volume one-half of its original volume. During the process, 300 kJ heat left the gas and the internal energy remained same. What is the work done on the gas?
A series combination of two Carnot's engines operates between the temperatures of $ 180^\circ\text{C} $ and $ 20^\circ\text{C} $. If the engines produce equal amount of work, then what is the intermediate temperature?
If a closed system is undergoing an irreversible process, the entropy of the system
The entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at
Increase in entropy of a system represents
Q.2 Solve both questions :
Define a thermodynamic system. Differentiate between open system, closed system and an isolated system with examples.
1 kg of a fluid is compressed reversibly according to a law $ pv = 0.25 $ where p is in bar and v is in $ \text{m}^3/\text{kg} $. The final volume is $ \frac{1}{4} $ of the initial volume. Calculate the work done on the fluid and sketch the process on a p-v diagram.
Q.3 Solve both questions :
0.15 $ \text{m}^3 $ of an ideal gas at a pressure of 15 bar and 550 K is expanded isothermally to 4 times the initial volume. It is then cooled to 290 K at constant volume and then compressed back polytropically to its initial state. Calculate net work done and heat transferred during the cycle.
0.2 $ \text{m}^3 $ of air at 4 bar and $ 130^\circ\text{C} $ is contained in a system. A reversible adiabatic expansion takes place till the pressure falls to 1.02 bar. The gas is then heated at constant pressure till enthalpy increases by 72.5 kJ. Calculate (i) the work done and (ii) the index of expansion, if the above processes are replaced by a single reversible polytropic process giving the same work between the same.
Q.4 Solve both questions :
With the help of p-v, T-s and p-T diagram, explain the nature of common salt (NaCl).
A spherical vessel of 0.9 $ \text{m}^3 $ capacity contains steam at 8 bar and 0.9 dryness fraction. Steam is blown off until the pressure drops to 4 bar. The valve is then closed and the steam is allowed to cool until the pressure falls to 3 bar. Assuming that the enthalpy of steam in the vessel remains constant during blowing-off periods, determine (i) the mass of steam blown-off; (ii) the dryness fraction of steam in the vessel after cooling and (iii) the heat lost by steam per kg during cooling.
Q.5 Solve both questions :
Give the following statements of second law of thermodynamics: (i) Clausius statement (ii) Kelvin-Planck statement
A reversible heat engine operates between two reservoirs at temperatures $ 700^\circ\text{C} $ and $ 50^\circ\text{C} $. The engine drives a reversible refrigerator which operates between reservoirs at temperatures of $ 50^\circ\text{C} $ and $ -25^\circ\text{C} $. The heat transfer to the engine is 2500 kJ and the net work output of the combined engine refrigerator plant is 400 kJ. (i) Determine the heat transfer to the refrigerant and the net heat transfer to the reservoir at $ 50^\circ\text{C} $; (ii) Reconsider (i) above given that the efficiency of the heat engine and the COP of the refrigerator are each 45 per cent of their maximum possible values.
Q.6 Solve both questions :
What do you mean by Clausius inequality? Explain with a practical example.
1 kg of air initially at 8 bar pressure and 380 K expands polytropically ($ pv^{1.2} = \text{constant} $) until the pressure is reduced to one-fifth value. Calculate (i) final specific volume and temperature; (ii) change of internal energy, work done and heat interaction and (iii) change in entropy. Take $ R = 0.287 \text{ kJ/kg K} $ and $ \gamma = 1.4 $.
Q.7 Solve both questions :
Explain the concept of available and unavailable energy. When does the system become dead?
Calculate the decrease in available energy when 20 kg of water at $ 90^\circ\text{C} $ mixes with 30 kg of water at $ 30^\circ\text{C} $, the pressure being taken as constant and the temperature of the surroundings being $ 10^\circ\text{C} $. Take $ C_p $ of water as 4.18 kJ/kg K.
Q.8 Solve both questions :
Differentiate between ideal and real gas with the help of equation of state.
(i) 1 kg of air at a pressure of 8 bar and a temperature of $ 100^\circ\text{C} $ undergoes a reversible polytropic process following the law $ pv^{1.2} = \text{constant} $. If the final pressure is 1.8 bar, determine- (1) the final specific volume, temperature and increase in entropy; (2) the work done and the heat transfer. Assume $ R = 0.287 \text{ kJ/kg K} $ and $ \gamma = 1.4 $. (ii) Repeat (a) assuming the process to be irreversible and adiabatic between end states.
Q.9 Solve both questions :
The readings from a sling psychrometer are as follows: Dry-bulb temperature = $ 30^\circ\text{C} $, Barometer reading = 740 mm of Hg. Using steam tables, determine (i) dew point temperature; (ii) relative humidity; (iii) specific humidity; (iv) degree of saturation; (v) vapour density and (vi) enthalpy of mixture per kg of dry air.
39.6 $ \text{m}^3/\text{min} $ of a mixture of recirculated room air and outdoor air enters cooling coil at $ 31^\circ\text{C} $ dry-bulb temperature and $ 18.5^\circ\text{C} $ wet-bulb temperature. The effective surface temperature of the coil is $ 4.4^\circ\text{C} $. The surface area of the coil is such as would give 12.5 kW of refrigeration with the given entering air state. Determine the dry- and wet-bulb temperatures of the air leaving the coil and the by-pass factor.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer from the following (any seven):
For reversible adiabatic compression in a steady flow process, the work transfer per unit mass is
Ice kept in a well insulated thermoflask is an example of which system?
Pressure reaches a value of absolute zero
Work done in a free expansion process is
Two blocks which are at different states are brought into contact with each other and allowed to reach a final state of thermal equilibrium. The final temperature attained is specified by the
A gas is compressed in a cylinder by a movable piston to a volume one-half of its original volume. During the process, 300 kJ heat left the gas and the internal energy remained same. What is the work done on the gas?
A series combination of two Carnot's engines operates between the temperatures of $ 180^\circ\text{C} $ and $ 20^\circ\text{C} $. If the engines produce equal amount of work, then what is the intermediate temperature?
If a closed system is undergoing an irreversible process, the entropy of the system
The entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at
Increase in entropy of a system represents
Q.2 Solve both questions :
Define a thermodynamic system. Differentiate between open system, closed system and an isolated system with examples.
1 kg of a fluid is compressed reversibly according to a law $ pv = 0.25 $ where p is in bar and v is in $ \text{m}^3/\text{kg} $. The final volume is $ \frac{1}{4} $ of the initial volume. Calculate the work done on the fluid and sketch the process on a p-v diagram.
Q.3 Solve both questions :
0.15 $ \text{m}^3 $ of an ideal gas at a pressure of 15 bar and 550 K is expanded isothermally to 4 times the initial volume. It is then cooled to 290 K at constant volume and then compressed back polytropically to its initial state. Calculate net work done and heat transferred during the cycle.
0.2 $ \text{m}^3 $ of air at 4 bar and $ 130^\circ\text{C} $ is contained in a system. A reversible adiabatic expansion takes place till the pressure falls to 1.02 bar. The gas is then heated at constant pressure till enthalpy increases by 72.5 kJ. Calculate (i) the work done and (ii) the index of expansion, if the above processes are replaced by a single reversible polytropic process giving the same work between the same.
Q.4 Solve both questions :
With the help of p-v, T-s and p-T diagram, explain the nature of common salt (NaCl).
A spherical vessel of 0.9 $ \text{m}^3 $ capacity contains steam at 8 bar and 0.9 dryness fraction. Steam is blown off until the pressure drops to 4 bar. The valve is then closed and the steam is allowed to cool until the pressure falls to 3 bar. Assuming that the enthalpy of steam in the vessel remains constant during blowing-off periods, determine (i) the mass of steam blown-off; (ii) the dryness fraction of steam in the vessel after cooling and (iii) the heat lost by steam per kg during cooling.
Q.5 Solve both questions :
Give the following statements of second law of thermodynamics: (i) Clausius statement (ii) Kelvin-Planck statement
A reversible heat engine operates between two reservoirs at temperatures $ 700^\circ\text{C} $ and $ 50^\circ\text{C} $. The engine drives a reversible refrigerator which operates between reservoirs at temperatures of $ 50^\circ\text{C} $ and $ -25^\circ\text{C} $. The heat transfer to the engine is 2500 kJ and the net work output of the combined engine refrigerator plant is 400 kJ. (i) Determine the heat transfer to the refrigerant and the net heat transfer to the reservoir at $ 50^\circ\text{C} $; (ii) Reconsider (i) above given that the efficiency of the heat engine and the COP of the refrigerator are each 45 per cent of their maximum possible values.
Q.6 Solve both questions :
What do you mean by Clausius inequality? Explain with a practical example.
1 kg of air initially at 8 bar pressure and 380 K expands polytropically ($ pv^{1.2} = \text{constant} $) until the pressure is reduced to one-fifth value. Calculate (i) final specific volume and temperature; (ii) change of internal energy, work done and heat interaction and (iii) change in entropy. Take $ R = 0.287 \text{ kJ/kg K} $ and $ \gamma = 1.4 $.
Q.7 Solve both questions :
Explain the concept of available and unavailable energy. When does the system become dead?
Calculate the decrease in available energy when 20 kg of water at $ 90^\circ\text{C} $ mixes with 30 kg of water at $ 30^\circ\text{C} $, the pressure being taken as constant and the temperature of the surroundings being $ 10^\circ\text{C} $. Take $ C_p $ of water as 4.18 kJ/kg K.
Q.8 Solve both questions :
Differentiate between ideal and real gas with the help of equation of state.
(i) 1 kg of air at a pressure of 8 bar and a temperature of $ 100^\circ\text{C} $ undergoes a reversible polytropic process following the law $ pv^{1.2} = \text{constant} $. If the final pressure is 1.8 bar, determine- (1) the final specific volume, temperature and increase in entropy; (2) the work done and the heat transfer. Assume $ R = 0.287 \text{ kJ/kg K} $ and $ \gamma = 1.4 $. (ii) Repeat (a) assuming the process to be irreversible and adiabatic between end states.
Q.9 Solve both questions :
The readings from a sling psychrometer are as follows: Dry-bulb temperature = $ 30^\circ\text{C} $, Barometer reading = 740 mm of Hg. Using steam tables, determine (i) dew point temperature; (ii) relative humidity; (iii) specific humidity; (iv) degree of saturation; (v) vapour density and (vi) enthalpy of mixture per kg of dry air.
39.6 $ \text{m}^3/\text{min} $ of a mixture of recirculated room air and outdoor air enters cooling coil at $ 31^\circ\text{C} $ dry-bulb temperature and $ 18.5^\circ\text{C} $ wet-bulb temperature. The effective surface temperature of the coil is $ 4.4^\circ\text{C} $. The surface area of the coil is such as would give 12.5 kW of refrigeration with the given entering air state. Determine the dry- and wet-bulb temperatures of the air leaving the coil and the by-pass factor.
Instructions:
- The marks are indicated in the right-hand margin.
- There are EIGHT questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Students should be allowed to use the steam tables and Mollier diagram.
Q.1 Choose the correct answer (any seven):
In a cycle
Zeroth law of thermodynamics forms the basis of
The cyclic integral of which of the following is zero?
Which one of the following parameters remains constant in a throttling process?
An isentropic process is always
A cyclic heat engine operates between a source temperature of $ 927^\circ\text{C} $ and a sink temperature of $ 27^\circ\text{C} $. What will be the maximum efficiency of the heat engine?
Which of the following expressions is true for Tds?
With increase in saturation pressure of water vapour
Availability function of a closed system is expressed as
At a pressure of 4 MPa, the temperature at which liquid water boils is
Q.2 Solve all questions :
Explain what you understand by thermodynamic equilibrium.
Distinguish between the terms 'change of state', 'path' and 'process'.
One mol of air at 0.45 MPa and 450 K initially undergoes the processes- (i) heating at constant pressure till the volume gets doubled and (ii) expansion at constant temperature till the volume is five times of initial volume sequentially. Determine the work done by air.
Q.3 Solve all questions :
Show that energy is a property of a system.
Write the steady flow energy equation for a single stream entering and a single stream leaving a control volume.
In a gas turbine the gas enters at the rate of 5 kg/s with a velocity of 50 m/s and enthalpy of 900 kJ/kg and leaves the turbine with a velocity of 150 m/s and enthalpy of 400 kJ/kg. The loss of heat from the gases to the surroundings is 25 kJ/kg. Assume for gas $ R = 0.285 \text{ kJ/kgK} $ and $ c_p = 1.004 \text{ kJ/kg-K} $ and the inlet conditions to be at 100 kPa and $ 27^\circ\text{C} $. Determine the power output of the turbine and the diameter of the inlet pipe.
Q.4 Solve both questions :
Establish the equivalence of Kelvin-Planck and Clausius statement.
An engine has a heat input of 500 kJ at $ 437^\circ\text{C} $. It rejects 200 kJ at $ 82^\circ\text{C} $. The engine develops 250 kJ of work. Check whether such an engine is possible or not.
Q.5 Solve both questions :
"Two reversible adiabatic paths cannot intersect each other." Write True or False. Justify with proper explanation.
A reversible engine operates between temperatures $ T_1 $ and $ T $, where $ T_1 > T $. The energy rejected from this engine is received by a second reversible engine at the same temperature $ T $. The second engine rejects energy at temperature $ T_2 $, where $ T_2 < T_1 $. Show that the temperature $ T $ is the arithmetic mean of temperatures $ T_1 $ and $ T_2 $ if the engines produce the same amount of work output.
Q.6 Solve both questions :
Establish the inequality of Clausius.
Steam flows in a pipeline at 1.5 MPa. After expanding to 0.1 MPa in a throttling calorimeter, the temperature is found to be $ 120^\circ\text{C} $. Find the quality of steam in the pipeline. What is the maximum moisture at 1.5 MPa that can be determined with this set-up if at least $ 5^\circ\text{C} $ of degree of superheat is required after throttling for accurate readings?
Q.7 Solve both questions :
What is meant by availability?
Air expands through a turbine from 500 kPa, $ 520^\circ\text{C} $ to 100 kPa, $ 300^\circ\text{C} $. During expansion 10 kJ/kg of heat is lost to the surroundings which is at 98 kPa, $ 20^\circ\text{C} $. Neglecting the KE and PE changes, determine per kg of air (i) the decrease in availability, (ii) the maximum work and (iii) the irreversibility. For air, take $ c_p = 1.005 \text{ kJ/kg-K} $, $ h = c_pT $ where $ c_p $ is constant.
Q.8 Solve all questions :
Define the terms 'unsaturated air' and 'relative humidity'.
With the help of a suitable diagram, explain the psychrometric chart.
With the help of a suitable diagram, explain the process of cooling and dehumidification.
Instructions:
- The marks are indicated in the right-hand margin.
- There are EIGHT questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Students should be allowed to use the steam tables and Mollier diagram.
Q.1 Choose the correct answer (any seven):
In a cycle
Zeroth law of thermodynamics forms the basis of
The cyclic integral of which of the following is zero?
Which one of the following parameters remains constant in a throttling process?
An isentropic process is always
A cyclic heat engine operates between a source temperature of $ 927^\circ\text{C} $ and a sink temperature of $ 27^\circ\text{C} $. What will be the maximum efficiency of the heat engine?
Which of the following expressions is true for Tds?
With increase in saturation pressure of water vapour
Availability function of a closed system is expressed as
At a pressure of 4 MPa, the temperature at which liquid water boils is
Q.2 Solve all questions :
Explain what you understand by thermodynamic equilibrium.
Distinguish between the terms 'change of state', 'path' and 'process'.
One mol of air at 0.45 MPa and 450 K initially undergoes the processes- (i) heating at constant pressure till the volume gets doubled and (ii) expansion at constant temperature till the volume is five times of initial volume sequentially. Determine the work done by air.
Q.3 Solve all questions :
Show that energy is a property of a system.
Write the steady flow energy equation for a single stream entering and a single stream leaving a control volume.
In a gas turbine the gas enters at the rate of 5 kg/s with a velocity of 50 m/s and enthalpy of 900 kJ/kg and leaves the turbine with a velocity of 150 m/s and enthalpy of 400 kJ/kg. The loss of heat from the gases to the surroundings is 25 kJ/kg. Assume for gas $ R = 0.285 \text{ kJ/kgK} $ and $ c_p = 1.004 \text{ kJ/kg-K} $ and the inlet conditions to be at 100 kPa and $ 27^\circ\text{C} $. Determine the power output of the turbine and the diameter of the inlet pipe.
Q.4 Solve both questions :
Establish the equivalence of Kelvin-Planck and Clausius statement.
An engine has a heat input of 500 kJ at $ 437^\circ\text{C} $. It rejects 200 kJ at $ 82^\circ\text{C} $. The engine develops 250 kJ of work. Check whether such an engine is possible or not.
Q.5 Solve both questions :
"Two reversible adiabatic paths cannot intersect each other." Write True or False. Justify with proper explanation.
A reversible engine operates between temperatures $ T_1 $ and $ T $, where $ T_1 > T $. The energy rejected from this engine is received by a second reversible engine at the same temperature $ T $. The second engine rejects energy at temperature $ T_2 $, where $ T_2 < T_1 $. Show that the temperature $ T $ is the arithmetic mean of temperatures $ T_1 $ and $ T_2 $ if the engines produce the same amount of work output.
Q.6 Solve both questions :
Establish the inequality of Clausius.
Steam flows in a pipeline at 1.5 MPa. After expanding to 0.1 MPa in a throttling calorimeter, the temperature is found to be $ 120^\circ\text{C} $. Find the quality of steam in the pipeline. What is the maximum moisture at 1.5 MPa that can be determined with this set-up if at least $ 5^\circ\text{C} $ of degree of superheat is required after throttling for accurate readings?
Q.7 Solve both questions :
What is meant by availability?
Air expands through a turbine from 500 kPa, $ 520^\circ\text{C} $ to 100 kPa, $ 300^\circ\text{C} $. During expansion 10 kJ/kg of heat is lost to the surroundings which is at 98 kPa, $ 20^\circ\text{C} $. Neglecting the KE and PE changes, determine per kg of air (i) the decrease in availability, (ii) the maximum work and (iii) the irreversibility. For air, take $ c_p = 1.005 \text{ kJ/kg-K} $, $ h = c_pT $ where $ c_p $ is constant.
Q.8 Solve all questions :
Define the terms 'unsaturated air' and 'relative humidity'.
With the help of a suitable diagram, explain the psychrometric chart.
With the help of a suitable diagram, explain the process of cooling and dehumidification.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Questions
Answer the following:
State zeroth law of thermodynamics and explain its utility in measuring temperature.
Explain the difference between microscopic and macroscopic form of energy. Give examples.
Write down the expressions for 'efficiency of heat engines', 'COP of refrigerator' and 'COP of heat pump' if all of them are operating between the same heat reservoirs.
How do the values of compare for a reversible and irreversible processes between the same end states?
Define 'availability'. Which of the two sources of energy viz., 'potential energy' and 'thermal energy' source possesses higher value of availability?
Why there is no constant temperature line in the wet region of Mollier diagram? Explain.
From the relationships given below, identify the relationship which is consequence of Helmholtz function $du = TdS - pdv$ $dg = -SdT + Vdp$ $dh = TdS + Vdp$ $da = -SdT - pdv$
Explain the difference between air-standard cycle and standard air-fuel cycle.
Which four processes constitute the simple ideal Rankine cycle? Sketch the cycle on T-S diagram.
Define absolute and relative humidity and give the relation between them.
Answer the following:
Does satisfying the first law of thermodynamics ensure that process will actually take place? Justify your answer by at least two examples.
Air enters adiabatic gas turbine at and and leaves it at and . The entry of air is through opening with an average velocity of and exhausts through opening. Determine the mass flow rate of air through the turbine and the power produced by the turbine.
Answer the following:
Show that there exists a property of a closed system such that change in its value is equal to for a reversible process undergone by the system between state '1' and '2'.
A piston cylinder device contains of nitrogen gas at and . The gas is now compressed slowly in a polytropic process during which . The process is stopped when the volume becomes half the original volume. Determine the change in entropy of nitrogen.
Answer the following:
Sketch the Carnot cycle for heat engine on a plane. Using this diagram, find out an expression for the thermal efficiency of the cycle.
A household refrigerator with a COP of 1.2 removes heat from refrigerated space at the rate of . Calculate (i) the electric power consumed by the refrigerator, (ii) heat transfer to the kitchen air and (iii) the higher temperature of the cycle if the average temperature in the refrigerator is .
Answer the following:
Define the following: (i) Compressed liquid (ii) Saturated liquid (iii) Superheated vapour (iv) Saturated vapour
A mass of wet steam at a temperature of with dryness fraction 0.80 is expanded to a pressure of 3 bar in such a way that quality remains the same. Isobaric heating is then adopted till the degree of superheat becomes . Find the enthalpy and entropy changes during the two processes. Draw the T-S and H-S diagrams.
Answer the following:
Name the basic ideal cycle for modern gas turbine and designate the different processes which constitute the cycle. Find out an expression for its thermal efficiency.
A reciprocating gasoline engine has a volumetric compression ratio of 8. The pressure and temperature of air before the compression begins are and . The combustion generates peak pressure of . Find the peak temperature, the energy added by combustion process and exhaust temperature.
Answer the following:
Explain the effect of reheat on (i) specific output, (ii) cycle efficiency, (iii) steam rate and (iv) heat rate of a steam power plant.
Steam enters a turbine at and , it expands in the turbine until it is dry and saturated and then it is reheated to . The condenser pressure is 0.04 bar. Calculate the work output and cycle efficiency assuming isentropic expansion and neglecting pump work. Also estimate the steam flow rate for an output of .
Answer the following:
State and explain Dalton's law of additive pressure and Amagat's law of additive volume for mixture of ideal gases. Also show that partial pressure fraction and volume fraction are equal to mole fraction.
A mixture consists of of and of . Calculate the mass of each gas and apparent gas constant of the mixture. Also calculate the density and volume of the mixture at and .
Answer the following:
Explain the meaning of (i) dry-bulb temperature, (ii) wet-bulb temperature, (iii) dew point and (iv) adiabatic saturation temperature.
The air in a room has a dry-bulb temperature of and wet-bulb temperature of . Assuming a pressure of , determine (i) specific humidity, (ii) relative humidity and (iii) dew point.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Students should be allowed to use the steam tables and Mollier diagram.
Q.1 Choose the correct answer from the following (any seven):
Ice kept in a wall-insulated thermoflask is an example of which system?
Which one of the following is the extensive property of a thermodynamic system?
In a general compression process, 1 kJ of mechanical work is supplied to 2 kg of fluid and 400 J of heat is rejected to the cooling jacket. The change in specific internal energy would be
First law of thermodynamics defines
Under what conditions, the change in the enthalpy of a system equals the heat supplied?
In a Carnot cycle, the rejection of heat is
A Carnot cycle is having an efficiency of 0.75. If the temperature of the high temperature reservoir is $ 727^\circ\text{C} $, what is the temperature of the low temperature reservoir?
Second law of thermodynamics defines
For a thermodynamic cycle to be irreversible, it is necessary that
Which of the following parameters remains constant during superheating of steam?
Q.2 Solve all questions :
State the first law of thermodynamics. What is PMM1?
Define quasi-static process.
The internal energy of a certain substance is given by the equation $ u = 3.56pv + 84 $, where u is given in kJ/kg, p is in kPa and v is in $ \text{m}^3/\text{kg} $. A system composed of 3 kg of this substance expands from an initial pressure of 500 kPa and a volume of 0.22 $ \text{m}^3 $ to a final pressure 100 kPa in a process in which pressure and volume are related by $ pv^{1.2} = \text{constant} $. If the expansion is quasi-static, find Q, $ \Delta U $, and W for this process.
Q.3 Solve both questions :
Derive an expression for conservation of energy for a steady flow process.
Consider a nozzle which is used to increase the velocity of a steady flowing stream. At the inlet to the nozzle, the enthalpy of fluid is 3000 kJ/kg and the velocity is 50 m/s. At the exit of the nozzle, the enthalpy is 2700 kJ/kg. The nozzle is kept horizontal and is well-insulated. (i) Find the velocity at the exit of the nozzle and the mass flow rate. (ii) If the inlet area is 0.12 $ \text{m}^2 $ and the sp. volume of the fluid at the inlet is 0.19 $ \text{m}^3/\text{kg} $, find the exit area of the nozzle, if the specific volume of the fluid at the exit is 0.5 $ \text{m}^3/\text{kg} $.
Q.4 Solve both questions :
State the Carnot theorem and explain with the help of suitable example.
Two reversible heat engines A and B are arranged in series, engine A rejecting heat directly to engine B. Engine A receives 180 kJ at a temperature of $ 422^\circ\text{C} $ from a hot source, while engine B is in communication with a cold sink at a temperature of $ 5.5^\circ\text{C} $. If the work output of A is twice that of B, find (i) the intermediate temperature between A and B, (ii) the efficiency of each engine and (iii) heat rejected to the cold sink.
Q.5 Solve both questions :
State and prove Clausius theorem.
Show that there is a decrease in available energy, when heat is transferred through a finite temperature difference.
Q.6 Solve all questions :
Show that the adiabatic mixing of two fluids is irreversible.
"An adiabatic process need not be isentropic, but if the process is adiabatic and reversible, it must be isentropic." Is it true or false? Explain with proper justification.
A reversible power cycle operates with temperature limits 800 K and 300 K. If it takes 480 kJ of heat, then what would be the unavailable work?
Q.7 Solve both questions :
What are various forms of energy?
Consider a system of cylinder and piston arrangement containing gas. Initially, the gas is at 500 kPa and occupies a volume of 0.2 $ \text{m}^3 $. The force exerted by the spring is proportional to the displacement from its equilibrium position. Take ambient pressure as 100 kPa. The gas is heated until the volume becomes 0.4 $ \text{m}^3 $ and the pressure attained as 1 MPa. Determine the work done by the gas. Draw the schematic and p-V diagram.
Q.8 Solve all questions :
What is the critical state? Draw the phase equilibrium diagram for a pure substance on h-s plot with relevant constant property lines.
Why do the isobars on Mollier diagram diverge from one another?
What is quality of steam? What are the different methods of measurement of quality of steam?
Q.9 Solve both questions :
Steam initially at 1.5 MPa, $ 300^\circ\text{C} $ expands reversibly and adiabatically in a steam turbine to $ 40^\circ\text{C} $. Determine the ideal work output of the turbine per kg of steam.
With the help of suitable diagram, explain heating and humidification.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Students should be allowed to use the steam tables and Mollier diagram.
Q.1 Choose the correct answer from the following (any seven):
Ice kept in a wall-insulated thermoflask is an example of which system?
Which one of the following is the extensive property of a thermodynamic system?
In a general compression process, 1 kJ of mechanical work is supplied to 2 kg of fluid and 400 J of heat is rejected to the cooling jacket. The change in specific internal energy would be
First law of thermodynamics defines
Under what conditions, the change in the enthalpy of a system equals the heat supplied?
In a Carnot cycle, the rejection of heat is
A Carnot cycle is having an efficiency of 0.75. If the temperature of the high temperature reservoir is $ 727^\circ\text{C} $, what is the temperature of the low temperature reservoir?
Second law of thermodynamics defines
For a thermodynamic cycle to be irreversible, it is necessary that
Which of the following parameters remains constant during superheating of steam?
Q.2 Solve all questions :
State the first law of thermodynamics. What is PMM1?
Define quasi-static process.
The internal energy of a certain substance is given by the equation $ u = 3.56pv + 84 $, where u is given in kJ/kg, p is in kPa and v is in $ \text{m}^3/\text{kg} $. A system composed of 3 kg of this substance expands from an initial pressure of 500 kPa and a volume of 0.22 $ \text{m}^3 $ to a final pressure 100 kPa in a process in which pressure and volume are related by $ pv^{1.2} = \text{constant} $. If the expansion is quasi-static, find Q, $ \Delta U $, and W for this process.
Q.3 Solve both questions :
Derive an expression for conservation of energy for a steady flow process.
Consider a nozzle which is used to increase the velocity of a steady flowing stream. At the inlet to the nozzle, the enthalpy of fluid is 3000 kJ/kg and the velocity is 50 m/s. At the exit of the nozzle, the enthalpy is 2700 kJ/kg. The nozzle is kept horizontal and is well-insulated. (i) Find the velocity at the exit of the nozzle and the mass flow rate. (ii) If the inlet area is 0.12 $ \text{m}^2 $ and the sp. volume of the fluid at the inlet is 0.19 $ \text{m}^3/\text{kg} $, find the exit area of the nozzle, if the specific volume of the fluid at the exit is 0.5 $ \text{m}^3/\text{kg} $.
Q.4 Solve both questions :
State the Carnot theorem and explain with the help of suitable example.
Two reversible heat engines A and B are arranged in series, engine A rejecting heat directly to engine B. Engine A receives 180 kJ at a temperature of $ 422^\circ\text{C} $ from a hot source, while engine B is in communication with a cold sink at a temperature of $ 5.5^\circ\text{C} $. If the work output of A is twice that of B, find (i) the intermediate temperature between A and B, (ii) the efficiency of each engine and (iii) heat rejected to the cold sink.
Q.5 Solve both questions :
State and prove Clausius theorem.
Show that there is a decrease in available energy, when heat is transferred through a finite temperature difference.
Q.6 Solve all questions :
Show that the adiabatic mixing of two fluids is irreversible.
"An adiabatic process need not be isentropic, but if the process is adiabatic and reversible, it must be isentropic." Is it true or false? Explain with proper justification.
A reversible power cycle operates with temperature limits 800 K and 300 K. If it takes 480 kJ of heat, then what would be the unavailable work?
Q.7 Solve both questions :
What are various forms of energy?
Consider a system of cylinder and piston arrangement containing gas. Initially, the gas is at 500 kPa and occupies a volume of 0.2 $ \text{m}^3 $. The force exerted by the spring is proportional to the displacement from its equilibrium position. Take ambient pressure as 100 kPa. The gas is heated until the volume becomes 0.4 $ \text{m}^3 $ and the pressure attained as 1 MPa. Determine the work done by the gas. Draw the schematic and p-V diagram.
Q.8 Solve all questions :
What is the critical state? Draw the phase equilibrium diagram for a pure substance on h-s plot with relevant constant property lines.
Why do the isobars on Mollier diagram diverge from one another?
What is quality of steam? What are the different methods of measurement of quality of steam?
Q.9 Solve both questions :
Steam initially at 1.5 MPa, $ 300^\circ\text{C} $ expands reversibly and adiabatically in a steam turbine to $ 40^\circ\text{C} $. Determine the ideal work output of the turbine per kg of steam.
With the help of suitable diagram, explain heating and humidification.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Students should be allowed to use the steam tables and Mollier diagram.
Questions
Choose the correct answer from the following (any seven):
Answer the following:
Answer the following:
Answer the following:
Answer the following:
Answer the following:
Answer the following:
Answer the following:
Answer the following:
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct option of the following (any seven):
Which of the following are intensive properties?
1. Kinetic energy
2. Specific enthalpy
3. Pressure
4. Entropy
Select the correct option using the code given below:
Ice kept in a well-insulated thermo-flask is an example of which system?
A gas contained in a cylinder is compressed, the work required for compression being 5000 kJ. During the process, heat interaction of 2000 kJ causes the surroundings to be heated. The change in internal energy of the gas during the process is
A reversible heat engine operating between hot and cold reservoirs delivers a work output of 54 kJ while it rejects a heat of 66 kJ. The efficiency of this engine is
A reversible engine operates between temperatures 900 K and $ T_2 $ ($ T_2 < 900 \text{ K} $), and another reversible engine between $ T_2 $ and 400 K ($ T_2> 400 \text{ K} $) in series. What is the value of $ T_2 $ if work outputs of both the engines are equal?
In a cyclic heat engine operating between a source temperature of $ 600^\circ\text{C} $ and a sink temperature of $ 20^\circ\text{C} $, the least rate of heat rejection per kW net output of the engine is
If a closed system is undergoing an irreversible process, the entropy of the system
A Carnot engine operates between $ 327^\circ\text{C} $ and $ 27^\circ\text{C} $. If the engine produces 300 kJ of work, what is the entropy change during heat addition?
A gas having a negative Joule-Thompson coefficient ($ \mu < 0 $), when throttled, will
Which one of the following represents the condensation of a mixture of saturated liquid and saturated vapour on the enthalpy-entropy diagram?
Q.2 Solve both questions :
Convert the following readings of pressure to kPa, assuming that the barometer reads 760 mmHg: (i) 90 cmHg gauge (ii) 40 cm Hg vacuum (iii) 1.2 m $ \text{H}_2\text{O} $ gauge (iv) 3.1 bar
The resistance of a platinum wire is found to be 11,000 ohms at the ice point, 15.247 ohms at the steam point, and 28.887 ohms at the sulphur point. Find the constants A and B in the equation $ R = R_0(1 + At + Bt^2) $ And plot R against t in the range 0 to $ 660^\circ\text{C} $.
Q.3 Solve both questions :
Show that heat and work are path functions and not a property. A single-cylinder, double-acting, reciprocating water pump has an indicator diagram which is a rectangle 0.075 m long and 0.05 m high. The indicator spring constant is 147 MPa per m. The pump runs at 50 r.p.m. The pump cylinder diameter is 0.15 m and the piston stroke is 0.20 m. Find the rate in kW at which the piston does work on the water.
State the first law of thermodynamics for a closed system undergoing a change of state. A gas of mass 1.5 kg undergoes a quasi-static expansion which follows a relationship $ p = a + bV $ where a and b are constants. The initial and final pressures are 1000 kPa and 200 kPa respectively and the corresponding volumes are 0.20 $ \text{m}^3 $ and 1.20 $ \text{m}^3 $. The specific internal energy of the gas is given by the relation $ u = 1.5pv - 85 \text{ kJ/kg} $, where p is the kPa and v is in $ \text{m}^3/\text{kg} $. Calculate the net heat transfer and the maximum internal energy of the gas attained during expansion.
Q.4 Solve both questions :
Derive the steady flow energy equation (SFEE). Under what conditions the SFEE does reduce to Euler's equation?
A turbo compressor delivers 2.33 $ \text{m}^3/\text{s} $ at 0.276 MPa, $ 43^\circ\text{C} $ which is heated at this pressure to $ 430^\circ\text{C} $ and finally expanded in a turbine which delivers 1860 kW. During the expansion, there is a heat transfer of 0.09 MJ/s to the surroundings. Calculate the turbine exhaust temperature if changes in kinetic and potential energy are negligible.
Q.5 Solve both questions :
A heat pump working on the Carnot cycle takes in heat from a reservoir at $ 5^\circ\text{C} $ and delivers heat to a reservoir at $ 60^\circ\text{C} $. The heat pump is driven by a reversible heat engine which takes in heat from a reservoir at $ 840^\circ\text{C} $ and rejects heat to a reservoir at $ 60^\circ\text{C} $. The reversible heat engine also drives a machine that absorbs 30 kW. If the heat pump extracts 17 kJ/s from the $ 5^\circ\text{C} $ reservoir, determine- (i) the rate of heat supply from the $ 840^\circ\text{C} $ source; (ii) the rate of heat rejection to the $ 60^\circ\text{C} $ sink.
What do you understand by exergy and energy? In a steam generator, water is evaporated at $ 260^\circ\text{C} $, while the combustion gas ($ C_p = 1.08 \text{ kJ/kg K} $) is cooled from $ 1300^\circ\text{C} $ to $ 320^\circ\text{C} $. The surroundings are at $ 30^\circ\text{C} $. Determine the loss in available energy due to the above heat transfer per kg of water evaporated (Latent heat of vaporization of water at $ 260^\circ\text{C} = 1662.5 \text{ kJ/kg} $).
Q.6 Solve both questions :
Give the criteria of reversibility, irreversibility and impossibility of a thermodynamic cycle. Two vessels, A and B, each of volume 3 $ \text{m}^3 $ may be connected by a tube of negligible volume. Vessel A contains air at 0.7 MPa, $ 95^\circ\text{C} $, while vessel B contains air at 0.35 MPa, $ 205^\circ\text{C} $. Find the change of entropy when A is connected to B by working from the first principles and assuming the mixing to be complete and adiabatic. Take $ C_p = 1.005 $ and $ C_v = 0.718 \text{ kJ/kg-K} $ and assume the specific heats to be constant. Also assume for air $ pv = 0.287 T $ where p is the pressure in kPa, v is the specific volume in $ \text{m}^3/\text{kg} $ and T is the temperature in K.
Show that the adiabatic mixing of two fluids is irreversible. Each of three identical bodies satisfies the equation $ U = CT $, where C is the heat capacity of each of the bodies. Their initial temperatures are 200 K, 250 K, and 540 K. If $ C = 8.4 \text{ kJ/K} $, what is the maximum amount of work that can be extracted in a process in which these bodies are brought to a final common temperature?
Q.7 Solve both questions :
Explain why the specific heat of a saturated vapour may be negative.
Explain, with suitable example, what is a pure substance? Draw the labelled phase equilibrium diagram for table salt on p-v, T-s and h-s coordinates. A large insulated vessel is divided into two chambers, one containing 5 kg of dry saturated steam at 0.2 MPa and the other 10 kg of steam, 0.8 quality at 0.5 MPa. If the partition between the chambers is removed and the steam is mixed thoroughly and allowed to settle, find the final pressure, steam quality and entropy change in the process.
Q.8 Solve both questions :
With the help of neat sketch, differentiate between the working of Otto and Diesel cycle.
A geothermal power plant utilizes steam produced by natural means underground. Steam wells are drilled to tap this steam supply which is available at 4.5 bar and $ 175^\circ\text{C} $. The steam leaves the turbine at 100 mmHg absolute pressure. The turbine isentropic efficiency is 0.75. Calculate the efficiency of the plant. If the unit produces 12.5 MW, what is the steam flow rate?
Q.9 Solve all questions :
What is the difference between specific and relative humidity? When does they become maximum?
Atmospheric air at dry bulb temperature of $ 15^\circ\text{C} $ enters a heating coil whose surface temperature is maintained at $ 40^\circ\text{C} $. The air leaves the heating coil at $ 25^\circ\text{C} $. What will be the by-pass factor of the heating coil?
For chemical reaction
$ \text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{CO} + \text{H}_2\text{O}
$
The equilibrium value of the degree of reaction at 1200 K is 0.56. Determine the equilibrium
constant and the Gibbs function change.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct option of the following (any seven):
Which of the following are intensive properties?
1. Kinetic energy
2. Specific enthalpy
3. Pressure
4. Entropy
Select the correct option using the code given below:
Ice kept in a well-insulated thermo-flask is an example of which system?
A gas contained in a cylinder is compressed, the work required for compression being 5000 kJ. During the process, heat interaction of 2000 kJ causes the surroundings to be heated. The change in internal energy of the gas during the process is
A reversible heat engine operating between hot and cold reservoirs delivers a work output of 54 kJ while it rejects a heat of 66 kJ. The efficiency of this engine is
A reversible engine operates between temperatures 900 K and $ T_2 $ ($ T_2 < 900 \text{ K} $), and another reversible engine between $ T_2 $ and 400 K ($ T_2> 400 \text{ K} $) in series. What is the value of $ T_2 $ if work outputs of both the engines are equal?
In a cyclic heat engine operating between a source temperature of $ 600^\circ\text{C} $ and a sink temperature of $ 20^\circ\text{C} $, the least rate of heat rejection per kW net output of the engine is
If a closed system is undergoing an irreversible process, the entropy of the system
A Carnot engine operates between $ 327^\circ\text{C} $ and $ 27^\circ\text{C} $. If the engine produces 300 kJ of work, what is the entropy change during heat addition?
A gas having a negative Joule-Thompson coefficient ($ \mu < 0 $), when throttled, will
Which one of the following represents the condensation of a mixture of saturated liquid and saturated vapour on the enthalpy-entropy diagram?
Q.2 Solve both questions :
Convert the following readings of pressure to kPa, assuming that the barometer reads 760 mmHg: (i) 90 cmHg gauge (ii) 40 cm Hg vacuum (iii) 1.2 m $ \text{H}_2\text{O} $ gauge (iv) 3.1 bar
The resistance of a platinum wire is found to be 11,000 ohms at the ice point, 15.247 ohms at the steam point, and 28.887 ohms at the sulphur point. Find the constants A and B in the equation $ R = R_0(1 + At + Bt^2) $ And plot R against t in the range 0 to $ 660^\circ\text{C} $.
Q.3 Solve both questions :
Show that heat and work are path functions and not a property. A single-cylinder, double-acting, reciprocating water pump has an indicator diagram which is a rectangle 0.075 m long and 0.05 m high. The indicator spring constant is 147 MPa per m. The pump runs at 50 r.p.m. The pump cylinder diameter is 0.15 m and the piston stroke is 0.20 m. Find the rate in kW at which the piston does work on the water.
State the first law of thermodynamics for a closed system undergoing a change of state. A gas of mass 1.5 kg undergoes a quasi-static expansion which follows a relationship $ p = a + bV $ where a and b are constants. The initial and final pressures are 1000 kPa and 200 kPa respectively and the corresponding volumes are 0.20 $ \text{m}^3 $ and 1.20 $ \text{m}^3 $. The specific internal energy of the gas is given by the relation $ u = 1.5pv - 85 \text{ kJ/kg} $, where p is the kPa and v is in $ \text{m}^3/\text{kg} $. Calculate the net heat transfer and the maximum internal energy of the gas attained during expansion.
Q.4 Solve both questions :
Derive the steady flow energy equation (SFEE). Under what conditions the SFEE does reduce to Euler's equation?
A turbo compressor delivers 2.33 $ \text{m}^3/\text{s} $ at 0.276 MPa, $ 43^\circ\text{C} $ which is heated at this pressure to $ 430^\circ\text{C} $ and finally expanded in a turbine which delivers 1860 kW. During the expansion, there is a heat transfer of 0.09 MJ/s to the surroundings. Calculate the turbine exhaust temperature if changes in kinetic and potential energy are negligible.
Q.5 Solve both questions :
A heat pump working on the Carnot cycle takes in heat from a reservoir at $ 5^\circ\text{C} $ and delivers heat to a reservoir at $ 60^\circ\text{C} $. The heat pump is driven by a reversible heat engine which takes in heat from a reservoir at $ 840^\circ\text{C} $ and rejects heat to a reservoir at $ 60^\circ\text{C} $. The reversible heat engine also drives a machine that absorbs 30 kW. If the heat pump extracts 17 kJ/s from the $ 5^\circ\text{C} $ reservoir, determine- (i) the rate of heat supply from the $ 840^\circ\text{C} $ source; (ii) the rate of heat rejection to the $ 60^\circ\text{C} $ sink.
What do you understand by exergy and energy? In a steam generator, water is evaporated at $ 260^\circ\text{C} $, while the combustion gas ($ C_p = 1.08 \text{ kJ/kg K} $) is cooled from $ 1300^\circ\text{C} $ to $ 320^\circ\text{C} $. The surroundings are at $ 30^\circ\text{C} $. Determine the loss in available energy due to the above heat transfer per kg of water evaporated (Latent heat of vaporization of water at $ 260^\circ\text{C} = 1662.5 \text{ kJ/kg} $).
Q.6 Solve both questions :
Give the criteria of reversibility, irreversibility and impossibility of a thermodynamic cycle. Two vessels, A and B, each of volume 3 $ \text{m}^3 $ may be connected by a tube of negligible volume. Vessel A contains air at 0.7 MPa, $ 95^\circ\text{C} $, while vessel B contains air at 0.35 MPa, $ 205^\circ\text{C} $. Find the change of entropy when A is connected to B by working from the first principles and assuming the mixing to be complete and adiabatic. Take $ C_p = 1.005 $ and $ C_v = 0.718 \text{ kJ/kg-K} $ and assume the specific heats to be constant. Also assume for air $ pv = 0.287 T $ where p is the pressure in kPa, v is the specific volume in $ \text{m}^3/\text{kg} $ and T is the temperature in K.
Show that the adiabatic mixing of two fluids is irreversible. Each of three identical bodies satisfies the equation $ U = CT $, where C is the heat capacity of each of the bodies. Their initial temperatures are 200 K, 250 K, and 540 K. If $ C = 8.4 \text{ kJ/K} $, what is the maximum amount of work that can be extracted in a process in which these bodies are brought to a final common temperature?
Q.7 Solve both questions :
Explain why the specific heat of a saturated vapour may be negative.
Explain, with suitable example, what is a pure substance? Draw the labelled phase equilibrium diagram for table salt on p-v, T-s and h-s coordinates. A large insulated vessel is divided into two chambers, one containing 5 kg of dry saturated steam at 0.2 MPa and the other 10 kg of steam, 0.8 quality at 0.5 MPa. If the partition between the chambers is removed and the steam is mixed thoroughly and allowed to settle, find the final pressure, steam quality and entropy change in the process.
Q.8 Solve both questions :
With the help of neat sketch, differentiate between the working of Otto and Diesel cycle.
A geothermal power plant utilizes steam produced by natural means underground. Steam wells are drilled to tap this steam supply which is available at 4.5 bar and $ 175^\circ\text{C} $. The steam leaves the turbine at 100 mmHg absolute pressure. The turbine isentropic efficiency is 0.75. Calculate the efficiency of the plant. If the unit produces 12.5 MW, what is the steam flow rate?
Q.9 Solve all questions :
What is the difference between specific and relative humidity? When does they become maximum?
Atmospheric air at dry bulb temperature of $ 15^\circ\text{C} $ enters a heating coil whose surface temperature is maintained at $ 40^\circ\text{C} $. The air leaves the heating coil at $ 25^\circ\text{C} $. What will be the by-pass factor of the heating coil?
For chemical reaction
$ \text{CO}_2 + \text{H}_2\text{O} \rightleftharpoons \text{CO} + \text{H}_2\text{O}
$
The equilibrium value of the degree of reaction at 1200 K is 0.56. Determine the equilibrium
constant and the Gibbs function change.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Questions
Answer the following:
In an open thermodynamic system (i) mass content of the system under consideration remains same (ii) transfer of mass and/or energy takes place (iii) there is only mass transfer even though there may not be any exchange of energy with the system environment (iv) the system exchanges energy with the surroundings in the form of heat energy only
Zeroth law of thermodynamics forms the basis of ______ measurement. (i) pressure (ii) temperature (iii) heat (iv) work
The cyclic integral of ($\delta Q - \delta W$) for a process is (i) zero (ii) positive (iii) negative (iv) unpredictable
Which one of the following parameters remains constant in a throttling process? (i) Pressure (ii) Temperature (iii) Enthalpy (iv) Entropy
The thermal efficiency of a Carnot engine is 30%. If the engine is reversed in operation to work as a heat pump (with no change in operating conditions), then what will be the COP of the heat pump? (i) 0.3 (ii) 2.33 (iii) 3.33 (iv) Cannot be calculated
A radiation shield should (i) have high transmissivity (ii) absorb all the radiations (iii) have high reflective power (iv) partly absorb and partly transmit the incident radiation
Which of the following expressions is true for Tds? (i) (ii) (iii) (iv)
With increase in saturation pressure of water vapour (i) the saturation temperature decreases (ii) the enthalpy of evaporation decreases (iii) the enthalpy of evaporation increases (iv) the specific volume of phase change increases
Which of the following processes is not associated with diesel cycle? (i) Constant volume (ii) Constant pressure (iii) Isothermal (iv) Adiabatic
A refrigerator based on reversed Carnot cycle works between two such temperatures that the ratio between the lowest and highest temperature is 0.8. If a heat pump is operated between same temperature range, then what would be its COP? (i) 5 (ii) 2 (iii) 3 (iv) 4
Answer the following:
What is the difference between a closed system and an open system?
Distinguish between the terms 'path function' and 'point function'.
A mass of 8 kg gas expands within a flexible container so that the relationship is of the form . The initial pressure is 1000 kPa and the initial volume is . The final pressure is 5 kPa. If specific internal energy of the gas decreases by , find the heat transfer in magnitude and direction.
Answer the following:
Write the steady flow energy equation for a single-stream entering and a single-stream leaving a control volume and explain the various terms in it.
Air at a temperature of passes through a heat exchanger at a velocity of where its temperature is raised to . It then enters a turbine with the same velocity of and expands until the temperature falls to . On leaving the turbine, the air is taken at a velocity of to a nozzle where it expands until the temperature has fallen to . If the air flow rate is , calculate (i) the rate of heat transfer to the air in the heat exchanger, (ii) the power output from the turbine assuming no heat loss, and (iii) the velocity at exit from the nozzle, assuming no heat loss.
Answer the following:
What are PMM1 and PMM2? Why are they impossible?
Two reversible heat engines A and B are arranged in series, A rejecting heat directly to B. Engine A receives 200 kJ at a temperature of from a hot source, while engine B is in communication with a cold sink at a temperature of . If the work output of A is twice that of B, find (i) the intermediate temperature between A and B, (ii) the efficiency of each engine, and (iii) the heat rejected to the cold sink.
Answer the following:
Show that heat transfer through a finite temperature difference is irreversible.
Show that the efficiency of a reversible engine operating between two given constant temperatures is the maximum.
A cyclic heat engine operates between a source temperature of and a sink temperature of , what is the least rate of heat rejection per kW net output of the engine?
Answer the following:
"Two reversible adiabatic paths cannot intersect each other", True or False. Justify with proper explanation.
A fluid undergoes a reversible adiabatic compression from , to according to the law, . Determine the change in enthalpy, internal energy and entropy, and the heat transfer and work transfer during the process.
Answer the following:
What are available energy and unavailable energy?
What do you understand by the degree of superheat and degree of subcooling?
Steam initially at , expands reversibly and adiabatically in a steam turbine to . Determine the ideal work output of the turbine per kg of steam.
Answer the following:
What is an air standard cycle? Why are such cycles conceived?
State the four processes of the Diesel cycle.
Derive the efficiency of the Otto cycle and show that it depends only on the compression ratio.
Answer the following:
With the help of and diagrams, show that for the same maximum pressure and temperature of the cycle and the same heat rejection, .
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Questions
Answer the following:
In a free expansion process involving ideal gas (i) (ii) (iii) (iv)
The efficiency of a Carnot engine is given as 0.75. If the cycle direction is reversed, what will be the value of COP of the Carnot refrigerator? (i) 0.271 (ii) 0.33 (iii) 1.27 (iv) 2.3
The first law of thermodynamics gives and second law tells that . In which of the way these two laws can be combined and written? (i) (ii) (iii) (iv)
With increase in pressure, the latent heat of steam (i) decreases (ii) increases (iii) remains the same (iv) behaves unpredictably
During dryness fraction measurement of steam using throttling calorimeter, the wet state of steam is throttled so as to lie in (i) wet state (ii) dry and saturated state (iii) superheated state (iv) supersaturated state
Air standard efficiency of Diesel cycle is a function of (i) compression ratio and cut-off ratio (ii) compression ratio and ratio of maximum to minimum temperature (iii) compression ratio and ratio of maximum to minimum pressure (iv) compression ratio and ratio of exhaust temperature to inlet temperature
The thermal efficiency of power plant lies in the range of (i) 20% to 30% (ii) 30% to 40% (iii) 40% to 50% (iv) 50% to 60%
Select the correct order for flue gas flow in a steam power plant layout. (i) Economiser, superheater and air-preheater (ii) Air-preheater, economiser and superheater (iii) Economiser, air-preheater and superheater (iv) Superheater, economiser and air-preheater
Humidity ratio can be expressed in terms of partial pressure of dry air ($p_a$) and water vapour ($p_v$) as (i) (ii) (iii) (iv)
Answer the following:
Derive the work done in process .
A mass of 8 kg gas expands within a flexible container so that the relationship is of the form . The initial pressure is 1000 kPa and the initial volume is . The final pressure is 5 kPa. If specific internal energy of the gas decreases by , then find the heat transfer in magnitude and direction.
Answer the following:
Describe indicator thermal efficiency and brake thermal efficiency.
A closed cylinder of 0.25 m diameter is fitted with a light frictionless piston. The piston is retained in position by a catch in the cylinder wall and volume on one side of the piston contains air at a pressure of . The volume on the other side of the piston is evacuated. A helical spring is mounted coaxially with the cylinder in this evacuated space to give a force of 120 N on the piston in this position. The catch is released and the piston travels along the cylinder until it comes to rest after a stroke of 1.2 m. The piston is then held in its position of maximum travel by a ratchet mechanism. The spring force increases linearly with the piston displacement to a final value of 5 kN. Calculate the work done by the compressed air on the piston.
Answer the following:
Describe a dual cycle.
An air-standard Diesel cycle, the compression ratio is 16, and at the beginning of isentropic compression, the temperature is and the pressure is 0.1 MPa. Heat is added until the temperature at the end of the constant pressure process is . Calculate (i) the cut-off ratio, (ii) the heat supplied per kg of air, (iii) the cycle efficiency and (iv) the mean effective pressure.
Answer the following:
Compare the Otto, Diesel and Dual cycle for same compression ratio.
In a steam power plant, the condition of steam at inlet to steam generator is 20 bar and and the condenser pressure is 0.1 bar. Two feed water heaters operate at optimum temperatures. Determine the (i) quality of steam at turbine exhaust, (ii) net work per kg, (iii) cycle efficiency and (iv) steam rate. Neglect pump work.
Answer the following:
Show that the decrease in available energy when heat is transferred through a finite temperature difference.
Define heat pump and refrigeration plant, and discuss their working principles with coefficient of performances.
Answer the following:
Define irreversibility and describe various causes of irreversibility.
A certain water heater operates under steady flow conditions receiving of water at temperature, enthalpy . The water is heated by mixing with the steam which is supplied to the heater at temperature and enthalpy . The mixture leaves the heater as liquid water at temperature and enthalpy . How much steam must be supplied to the heater per hour?
Answer the following:
Describe different modes of energy storage in a thermodynamic system.
Describe the terms 'specific heat at constant volume', 'enthalpy' and 'specific heat at constant pressure'.
Answer the following:
A vessel of volume contains a mixture of saturated water and saturated steam at a temperature of . The mass of the liquid present is 9 kg. Find the pressure, the mass, the specific volume, the enthalpy, the entropy and the internal energy. Use the steam table.
Write four Maxwell's equations.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Questions
Answer the following:
The difference between the pressure of fluid and the pressure of atmosphere is called as (a) Barometric pressure (b) Absolute pressure (c) Gauge Pressure (d) None of these
Which of the following sets has all properties as point functions? (a) Entropy, enthalpy, work (b) Pressure, temperature, heat (c) Heat, work, enthalpy (d) Temperature, enthalpy, internal energy
Which of the following sets has all open systems? (a) Boiler, gas turbine, compressor, condenser (b) Pump, thermo-flask, refrigerator, petrol engine (c) Window air conditioner, scooter engine, thermometer, diesel engine (d) Jet engine, gas engine, pressure cooker, steam turbine
The elastic work ($\delta W$) per unit volume required for stretching a wire of length is given by the expression (a) (b) (c) (d) None of the above
The thermometric property of electrical resistance thermometer is (a) Current (b) Potential difference (c) Magnetic (d) Resistance
The internal energy for a perfect gas is expressed as (a) (b) (c) (d)
The following amount of heat transfer occurs during a cycle comprising of four processes. $120 \text{ kJ, } -20 \text{ kJ, } 16 \text{ kJ, and } 24 \text{ kJ}$ (a) 100 kJ (b) 120 kJ (c) 130 kJ (d) 140 kJ
The Van der waals equation of state for real gases may by given by (a) (b) (c) (d)
Select the correct relation (a) (b) (c) (d) All of these
Answer the following:
Describe Thermodynamic Equilibrium and Quasi-static process.
An air standard dual cycle has a compression ratio of 16 and compression begins at 1 bar, 50 ^\circ$C. The maximum pressure is 70 bar. The heat transferred to air at constant pressure is equal to that at constant volume. Estimate (a) the pressure and temperatures at the cardinal points of the cycle, (b) the cycle efficiency (Given: for air $\gamma = 1.4, kJ/kg-K, and kJ/kg-K).
Answer the following:
What are the four processes which constitute the Carnot cycle. A Carnot cycle operates between 0 $^\circ$C and 100 $^\circ$C. Determine thermal efficiency, if it operates as a heat engine and COPs if it operates as Heat pump and Refrigerator.
Describe Rankine Cycle? Define quality and dryness fraction of steam.
Answer the following:
Describe and Diesel Cycle.
A steam power plant operates on a simple ideal Rankine cycle between the pressure limits of 25 bar and 0.10 bar and handles 2 kg of steam. The temperature of steam at turbine inlet is 360 $^\circ$C. The steam enters a condenser and after condensation, the pump feeds back the steam into boiler. Show (a) p-v diagram with saturation lines; (b) T-S diagram with saturation lines; and calculate (c) the thermal efficiency of the cycle, (d) the net power output of the power plant, (e) the work ratio.
Answer the following:
Show the equivalence between statements of Kelvin-Planck and Clausius for 2nd law of thermodynamics.
Derive the Inequality of Clausius as an criterion of reversibility of irreversibility of a thermodynamic cycle.
Answer the following:
Draw p-v diagram for polytropic process , for n=0, n=1, n=2 \text{ & } n=\infty under expansion and compression processes.
A vessel of volume 0.04 m$^3$ contains a mixture of saturated water and saturated steam at a temperature of 250 $^\circ$C. The mass of the liquid present is 9 kg. Find the pressure, the mass, the specific volume, the enthalpy, the entropy and the internal energy. Use the Steam Table.
Answer the following:
Describe Available and Unavailable energy.
What are Helmholtz's and Gibb's functions. Write four Maxwell's Equations.
Answer the following:
Derive equation of efficiency for ideal Otto Cycle i.e. . In an ideal Otto cycle, the air at the beginning of isentropic compression is at 1 bar and 15 $^\circ$C. The ratio of compression is 8. If the heat added during the constant volume process is 1000 kJ/kg then determine (i) the air standard efficiency; (ii) work done; (iii) heat rejected; (iv) maximum temperature of air during the cycle.
A reversible heat engine operates between two reservoirs at temperatures of 600 ^\circ$C. The engine drives a reversible refrigerator which operates between reservoirs at temperatures of 40 $^\circ$C and $-20 $^\circ$C. The heat transfer to the heat engine is 2000 kJ and the net work output of the combined engine refrigerator plant is 360 kJ. (a) Evaluate the heat transfer to the refrigerant and the net heat transfer to the reservoir at 40 $^\circ$C. (b) Reconsider (a) given that the efficiency of the heat engine and the COP of the refrigerator are each 40% of their maximum possible values.
Answer the following:
Using the steady flow energy equation, find the work done in Turbine and compressor.
Derive a steady state energy flow equation for any thermodynamic system operating under control volume and control surface.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Questions
Answer the following:
Isolated system has fixed mass and energy. (True/False)
Specific volume is the extensive property of a thermodynamic system. (True/False)
A gas performs no work in the process of free expansion. (True/False)
Change in the internal energy of a closed system is equal to the heat transferred in a constant volume process involving no work other than p.d.v. work. (True/False)
Enthalpy of the fluid before throttling is not equal to the enthalpy of the fluid after throttling. (True/False)
Work is said to be a low grade energy and heat a high grade energy. (True/False)
The cyclic integral of for a reversible cycle is greater than zero. (True/False)
The slop of an isobar on Mollier diagram is equal to the absolute temperature. (True/False)
Heat addition process in the Rankine cycle is reversible and at constant process whereas in the Carnot cycle it is reversible and isothermal. (True/False)
For same maximum pressure, temperature and heat rejection, the efficiency of Diesel cycle is greater than efficiency of Otto cycle. (True/False)
Answer the following:
Explain thermodynamic equilibrium.
Explain Quasi-static process briefly.
Determine the total work done by a gas system following an expansion process as shown in the figure (Note: Points A(10.2, 50) and B(10.4, 50) on p-V plane, then polytropic expansion to $V = 10.8$).
Answer the following:
Air flows steadily at the rate of 0.8 kg/s through an air compressor, entering at 10 m/s velocity, 100 kPa pressure and volume and leaving at 8 m/s, 700 kPa and . The internal energy of the air leaving is 100 kJ/kg greater than that of the air entering. Cooling water in the compressor jackets absorbs heat from the air at the rate of 60 kW. (i) compute the rate of shaft work input to the air in kW and (ii) find the ratio of the inlet pipe diameter to the outlet pipe diameter.
Answer the following:
A reversible heat engine operates between two reservoirs at temperatures of 900 K and 400 K. The engine drives a reversible refrigerator which operates between 400 K and 250 K. The heat transfer to the heat engine is 2000 kJ and the net work output of the combined engine refrigerator plant is 400 kJ. (a) Evaluate the heat transfer to the refrigerator and the net heat transfer to the reservoir at 400 K. (b) If the efficiency of the heat engine and the COP of refrigerator are each 60% of their maximum possible value, evaluate the heat transfer to the refrigerator and the net heat transfer to the reservoir at 400 K.
Answer the following:
Explain and prove Carnot's theorem.
One kg of water at 283 K is brought into contact with a heat reservoir at 363 K. When the water has reached 363 K, find the entropy change of the universe. If water is heated from 283 K to 363 K by first bringing it in contact with a reservoir at 333 K and then with a reservoir at 363 K. what will the entropy change of the universe be? Comment on the two different values of entropy change of the universe.
Answer the following:
Derive and explain Maxwell's four equations.
Steam initially at 15 bar, 573 K expands isoentropically in a steam turbine to 313 K. Determine the ideal work output of the turbine per kg of steam.
Answer the following:
Derive the expression of thermal efficiency of a Diesel cycle and with the help of P-V and T-S diagrams. Compare the thermal efficiencies of Otto cycle and Diesel cycle for the same compression ratio and heat rejection.
Answer the following:
A steam power station uses the following cycle : Steam at turbine inlet: 150 bar, 550 $^\circ$C. reheat at 40 bar to same boiler outlet temperature. Condenser at 0.1 bar. Assuming ideal processes, find the— (a) quality of steam at turbine exhaust; (b) cycle efficiency; (c) steam rate.
Answer the following:
One kg of dry air at 20 $^\circ$C and 40% RH is mixed adiabatically with two kg of dry air at 40 $^\circ$C and 40% RH. Find the final condition of air.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Questions
Answer the following:
Volume is the extensive property of a thermodynamic system. (True/False)
A closed system is one in which neither mass nor energy cross the boundary of the system. (True/False)
If the reversible process takes place at constant pressure, change in enthalpy in a closed system is equal to the heat transfer. (True/False)
A real gas obeys perfect gas law at very high temperature and low pressure. (True/False)
The entropy of universe tends to zero. (True/False)
The Clausius-Clapeyron equation gives the slope of a curve in p-T diagram. (True/False)
The state of a wet vapour cannot be specified only by pressure and dryness fraction. (True/False)
When DBT, WBT and DPT are identical it means that the air is saturated. (True/False)
In a Rankine cycle heat is rejected reversibly at constant volume. (True/False)
A gas turbine works on Brayton cycle. (True/False)
Answer the following:
State and explain zeroth law of thermodynamics.
One kg of air at 1 bar and 300 K is compressed adiabatically till its pressure becomes 5 times the original pressure. Then it is expanded at constant pressure and finally cooled at constant volume to return to its original state. Calculate heat transfer, work transfer and change in internal energy for each process and for the cycle.
Answer the following:
Air at 288 K passes through a heat exchanger at a velocity of 30 m/s where its temperature is raised to 1073 K. It then enters a turbine with the same velocity of 30 m/s and expands until the temperature falls to 923 K. On leaving the turbine, air is taken at a velocity of 60 m/s to a nozzle where it expands until the temperature has fallen to 773 K. Calculate for the air flow rate of 2 kg/s—(a) the rate of heat transfer to the air in the heat exchanger; (b) the power output from the turbine assuming no heat loss and (c) the velocity at exit from the nozzle assuming no heat loss.
Answer the following:
Show that the COP of a heat pump is greater than the COP of a refrigerator by unity.
A heat engine working on Carnot cycle exchanges heat from three reservoirs at 200 K, 300 K and 400 K. If it draws 5 MJ from the 400 K reservoir and does 840 kJ of work during a cycle of operation, find the amount and direction of heat interaction with other reservoirs.
Answer the following:
An inventor claims to have designed an engine which receives 2.5 kJ of heat and produces 0.625 kJ of useful work between source at 60 $^\circ$C and sink at 263 K. Is this claim valid?
m kg of air at is adiabatically mixed with same mass of air at in a container. Find the change of entropy and prove that this change is always positive.
Answer the following:
Derive the expression of thermal efficiency of diesel cycle.
With the help of p-v and T-s diagrams, show that for the same maximum pressure and temperature of the cycle .
Answer the following:
A vessel of volume 0.04 m$^3$ contains a mixture of saturated water and saturated steam at a temperature of 250 $^\circ$C. The mass of the liquid present is 9 kg. Find the pressure, mass, specific volume, enthalpy, entropy and internal energy.
Answer the following:
Steam at 20 bar, 360 $^\circ$C is expanded in a steam turbine plant to 0.08 bar. If the plant works on Rankine cycle, find network and cycle efficiency. If the turbine and pump have each 80% efficiency, find the percentage change in net-work cycle efficiency.
Answer the following:
120 m$^3$/min of air at 35 $^\circ$C DBT and 45% RH is adiabatically mixed with 325 m$^3$/min of air at 20 $^\circ$C DBT and 10 $^\circ$C DPT. Determine the specific humidity, DBT, and DPT of the mixture without using psychrometric chart.
Instructions:
- All questions carry equal marks.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Use of Tables and Charts permitted.
Q.1 State whether the following statements are True or False (any seven):
Zeroth law of the thermodynamics defines temperatures.
Characteristic equation of gas is given by ( = specific volume, = mass of gas) .
Otto cycle consists of two constant volumes and two adiabatic processes.
Internal energy of ideal gas is a function of temperature and volume.
One of the equations has the form .
The entropy of fixed amount of ideal gas increases in every isothermal compression.
At triple point, ice occupies maximum specific volume.
The specific volume of water when heated from , first increases then decreases.
The relationship between and for the same range of temperature operation is .
Standard Barometric pressure is 1013.25 M bar.
Q.2 Solve the following :
What do you mean by closed system and open system? Explain.
Q.3 Solve the following :
What do you mean by temperature? What are the common scales used for measuring the temperature of human body?
What do you mean by thermodynamic equilibrium? What is equality of temperatures?
Q.4 Solve the following :
0.5 kg of a perfect gas is heated from to at a constant pressure of 2.8 bar. It is then cooled to at constant volume. Find the overall change in entropy. Take , .
An inventor claims to have heat engine which is capable of developing 19 kW while working between the temperature limits and . It receives only 1000 kJ/min of heat. Discuss the possibility of the claim.
Q.5 Solve the following :
What are Helmholtz function and Gibb's function?
Q.6 Solve the following :
List the assumptions made in the analysis of air-standard cycle.
With the help of and diagrams show that for the same compression ratio and same heat input .
Q.7 Solve the following :
In a thermal power plant operating on an Ideal Rankine cycle, steam of 15 bar and enters a turbine which generates 40 kW indicated power. If the steam consumption is 300 kg/hr and condenser is maintained at 0.15 bar, determine the final condition of steam, Rankine efficiency and relative efficiency. Neglect pump work. Also determine the fuel to be supplied/hr if its is 41850 kJ/kg.
Q.8 Solve the following :
Define and explain the terms in relation to psychrometry.
Dry bulb, wet bulb and dew point temperature
Relative humidity and specific humidity
Q.9 Solve the following :
A mixture of 1 kg of oxygen and 2 kg of nitrogen occupies volume of temperature 300 K. Assuming perfect gas behaviour, determine the following:
Specific volume
Pressure
Gas constant
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Questions
Answer the following:
Define thermodynamic system and give its classification.
Explain the difference between energy interaction as 'heat' and 'work', and give their common characteristics.
Showing the direction of heat flow, distinguish between a 'heat engine' and a 'heat pump'.
Is the value of integral same for all the processes between state 1 and state 2? Explain.
Two heat engines A and B have the same thermal efficiency of 30%. The sink temperature for both of them is 300 K, whereas the source temperature for A is 600 K and for B it is 1000 K. Which one is performing better?
Why do constant temperature lines on Mollier diagram become parallel to abscissa in the superheated region at low pressure?
From the relationships given below, identify the relation which is consequence of Gibbs' function : (i) (ii) (iii) (iv)
Give five important assumptions for air standard cycle in case of IC engines.
Give the effect of lowering the condenser pressure in case of a simple Rankine cycle on turbine work output, cycle efficiency and pump work input.
When are the adiabatic saturation and wet-bulb temperatures equivalent for atmospheric air?
Answer the following:
State and explain the first law of thermodynamics.
Two air flows are combined to a single flow. The inlet pressure for the stream is 100 kPa. The flow rate for one is 1 m$^3$/s at 293 K, while for the other it is 2 m$^3$/s at 473 K. The mixing takes place in a horizontal mixture without any heat transfer. Neglecting kinetic energy, find the volume flow rate and temperature of air at exit pressure of 100 kPa.
Answer the following:
Prove that entropy of a closed system, which is thermally insulated from the surroundings, either increases or remains constant if the process is reversible.
1 kg of air expanded reversibly in a cylinder behind a piston isothermally maintaining the temperature at 530 K till the volume gets doubled. The piston is then pushed back at constant pressure till the original volume is restored. Sketch the processes on T-S plane having constant temperature and constant pressure lines also. Calculate the change in entropy and heat flow for each process and overall.
Answer the following:
What do you understand by a reversible process? Distinguish among internally, externally and totally reversible processes. Whether the process has to be quasistatic? Justify.
A Carnot engine, with air as working fluid, operates between maximum and minimum pressures of 6.25 MPa and 0.104 MPa. The limiting temperatures being 580 K and 290 K, find (i) thermal efficiency, and (ii) work ratio for the cycle. Sketch the cycle on p-v and T-S planes.
Answer the following:
Define the following : (i) Saturation pressure (ii) Saturation temperature (iii) Degree of superheat (iv) Liquid-vapour saturation curve
A closed system consists of 1 kg of steam. This system undergoes three different reversible processes to constitute a thermodynamic cycle. The initial condition of steam pressure is 10 bar and . The process 1–2 is constant volume heating till pressure becomes 35 bar. The process 2–3 is isothermal expansion up to pressure of 10 bar. The process 3–1 is constant pressure cooling to bring the system back to its initial state. Sketch the cycle on Mollier diagram. For each process, calculate (i) entropy change, (ii) heat transfer, and (iii) work done. Also find cycle efficiency.
Answer the following:
Identify ideal cycle for spark-ignition reciprocating engine and name the process involved in it. Also find the expression for its cycle efficiency.
A diesel engine has a compression ratio of 20 : 1. The pressure, temperature and volume at the beginning of compression are 95 kPa, 290 K and 0.50 litre respectively. The maximum cycle temperature is 1800 K. Find the cycle efficiency and maximum pressure.
Answer the following:
Why is Carnot cycle not a realistic model for steam power plant? Name the cycle suitable for steam power plant and plot the same on T-S diagram.
In a reheat cycle, the initial steam pressure and maximum temperature are 150 bar and 550 $^\circ$C respectively. If the condenser pressure is 0.1 bar and moisture at condenser inlet is 5%, find (i) reheat pressure, (ii) cycle efficiency, and (iii) steam flow rate in kg/kW-h assuming ideal processes. Neglect pump work.
Answer the following:
Define 'mole fraction' and 'mass fraction' in a mixture of nonreacting ideal gases and establish a relationship between them for a mixture of two gases.
A mixture of ideal gases at a pressure of 150 kPa and 40 ^\circ$C contains 8 kg of nitrogen and 5 kg of oxygen. Determine for the mixture (i) average molecular weight, (ii) specific gas constant, and (iii) the two specific heats, $C_p and for nitrogen may be taken as 0.70 kJ/kg-K and 1.037 kJ/kg-K, whereas for oxygen it is 0.75 kJ/kg-K and 1.04 kJ/kg-K.
Answer the following:
Define absolute humidity and relative humidity, and establish a relation between them.
Consider 100 m$^3$ of atmospheric air which is an air-water vapour mixture at 100 kPa and 40 $^\circ$C having a relative humidity of 40%. Find the (i) mass of dry air, (ii) mass of vapour, (iii) specific humidity, and (iv) dew point. Also calculate the amount of water condensed if the mixture is cooled to 10 $^\circ$C.
Instructions:
- All questions carry equal marks.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
- Use of Tables and Charts permitted.
Q.1 State whether the following statements are True or False (any seven):
The sum of internal energy and pressure volume product is called enthalpy.
Diesel cycle consists of two constant volumes and two adiabatic processes.
For the same compression ratio and same heat input the thermal efficiency of Otto cycle is less than that of Diesel cycle.
Intensive properties are independent of the mass of the system.
An isolated system is one which permits the passage of energy only.
Liquids have two specific heats.
Thermal power plant works on Rankine cycle.
Sublimation is the process of changing from solid state to direct gas state.
On psychrometric chart, DBT lines are horizontal.
During sensible cooling process, specific humidity decreases.
Q.2 Solve the following :
State and explain zeroth law of thermodynamics.
Derive an expression of displacement work for an adiabatic process.
What do you mean by flow work?
Q.3 Solve the following :
Show that the efficiency of all reversible heat engines operating between the same temperature levels is the same.
What is a Carnot cycle? Derive its efficiency with the help of diagram and block diagram.
Q.4 Solve the following :
2 kg of ice at is exposed to the atmosphere which is at . The ice melts and comes into thermal equilibrium with the atmosphere. Determine—
the entropy increase of the universe;
the minimum amount of work necessary to convert the water back into ice at .
Q.5 Solve the following :
What do you mean by triple point?
A large insulated vessel is divided into two compartments, one containing 5 kg of dry saturated steam at 2 bar and the other 10 kg of steam, 0.8 dry at 5 bar. If the partition is removed and the steam is mixed thoroughly and allowed to settle, find the final pressure, steam quality and entropy change.
Q.6 Solve the following :
What is the reversible cycle that represents the simple steam power plant? Draw the flow, , and diagrams of this cycle.
What do you understand by the mean temperature of heat addition?
How are the maximum temperature and maximum pressure in the Rankine cycle fixed?
Q.7 Solve the following :
Develop an expression for the thermal efficiency of an air-standard Diesel cycle.
Compare the efficiency of Otto, Diesel and dual cycles in the following cases with the help of and diagrams:
For the same compression ratio
For the same maximum pressure and temperature
Q.8 Solve the following :
3 kg of air at DBT and WBT is adiabatically mixed with 2 kg of air at DBT and DPT. Determine the final specific humidity and temperature of the mixture without using psychrometric chart.
Q.9 Solve the following :
A mixture of ideal gases consists of 2 kg of and 4 kg of at a pressure of 3 bar and temperature of . If the mixture is heated at constant pressure to ( 50^\circ\text{C} , find the change in entropy of the mixture.
Write the Maxwell's equations.
Instructions:
- The marks are indicated in the right-hand margin.
- There are NINE questions in this paper.
- Attempt FIVE questions in all.
- Question No. 1 is compulsory.
Q.1 Choose the correct answer (any seven):
In case of free expansion between state-1 and state-2, which of the following is correct considering no heat interaction?
The latent heat of vaporisation with increase in pressure of water
As differentials heat and work would be described mathematically as
Heat is being supplied to air in a cylinder fitted with a frictionless piston held by a constant weight, the process is
Expansion of hot gases in an IC engine can be approximated to an
A refrigerator and a heat pump operate between same temperature limits. If the COP of refrigerator is 4, then the COP of heat pump is
A relation of vapour pressure to enthalpy of vaporisation is expressed in
For same maximum pressure and temperature among Otto, diesel and dual cycles
Thermal efficiency of Rankine cycle can be improved by steam
The process of removing moisture from air at constant dry-bulb temperature is known as
Q.2 Solve the following :
Define internal energy. Show that internal energy is a property of a system.
A cylinder contains of air at 1 bar and . It is compressed to . The final pressure being 6 bar. Find the index of compression, increase in internal energy and heat transferred. Take and .
Q.3 Solve the following :
Prove that the Kelvin-Planck and Clausius statement of the second law of thermodynamics are equivalent to each other.
A reversed Carnot cycle operating as a refrigerator has a refrigerating capacity of 100 kJ/s while operating between temperature limits of and . Determine (i) power input and (ii) COP. What would be its efficiency if it runs as an engine?
Q.4 Solve the following :
State and prove Clausius inequality.
During isothermal heat addition process of a Carnot cycle, 800 kJ heat is added to the working fluid from a source of . Determine (i) change in entropy of the working fluid, (ii) change in entropy of the source and (iii) total entropy change during the process.
Q.5 Solve the following :
Define the following:
Pure substance
Saturation state
Triple point and critical point
A vessel of volume contains a mixture of saturated water and saturated steam at a temperature of . The mass of liquid is 9 kg. Find the pressure, the mass, the specific volume, the enthalpy, the entropy and the internal energy.
Q.6 Solve the following :
In an air-standard dual cycle, the pressure and temperature at beginning of compression are 1 bar and respectively. The heat supplied in the cycle is 1250 kJ/kg, two-third of this being added at constant volume and rest at constant pressure. If the compression ratio is 16, determine the air-standard efficiency.
Q.7 Solve the following :
Give limitation of Carnot vapour power cycle and explain how Rankine cycle helps in overcoming them.
A steam power plant running on Rankine cycle has steam entering HP turbine at 20 MPa, and leaving LP turbine at 90% dryness. Considering condenser pressure of 0.005 MPa and reheating occurring up to the temperature of , determine the thermal efficiency of the cycle.
Q.8 Solve the following :
What do you understand by dry-bulb and wet-bulb temperatures? When do d.b.t., w.b.t. and d.p.t. become equal?
of air at 1 atm and with 90% RH is mixed with of air at 1 atm and with 20% RH. Calculate the resulting state of mixture.
Q.9 Solve the following :
Explain Maxwell relation in thermodynamics.
A gaseous mixture consists of 1 kg of oxygen and 2 kg of nitrogen at a pressure of 150 kPa and a temperature of . Determine the change in internal energy and enthalpy of the mixture when the mixture is heated to a temperature of (i) at constant volume and (ii) at constant pressure.