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2023 101407

End Semester Examination - 2023 (Semester-IV)

Time 03 Hours
Full Marks 70
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 of the following (Any seven question only):

Q1.1

Which one of the following is the extensive property of thermodynamic system?

a)

Volume

b)

Pressure

c)

Temperature

d)

Density

Q1.2

Ice kept in a well-insulated thermosflask is an example of which system?

a)

Closed System

b)

Isolated System

c)

Open System

d)

Non-flow adiabatic system

Q1.3

Measurement of temperature is based on which law of thermodynamics?

a)

Zero law of thermodynamics

b)

First law of thermodynamics

c)

Second law of thermodynamics

d)

Third law of thermodynamics

Q1.4

A closed system receives 60 kJ heat but its internal energy decreases by 30 kJ. Then the work done by the system is

a)

90 kJ

b)

30 kJ

c)

-30 kJ

d)

-90 kJ

Q1.5

A reversible engine operates between temperature 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. The value of $ T_{2} $ if work outputs of both the engines are equal is

a)

600 K

b)

625 K

c)

650 K

d)

675 K

Q1.6

For real thermodynamics cycle, which one of the following is correct?

a)

\oint \frac{dQ}{T} &gt; 0

b)

\oint \frac{dQ}{T} &lt; 0

c)

dQT=0\oint \frac{dQ}{T} = 0

d)

ds=0\oint ds = 0

Q1.7

The specific volume of water when heated from $ 0^{\circ}C $

a)

first increases and then decreases

b)

increases steadily

c)

decreases and then increases

d)

decreases steadily

Q1.8

A four-stroke petrol engine theoretically operates on

a)

Otto Cycle

b)

Brayton Cycle

c)

Joule Cycle

d)

Rankine Cycle

Q1.9

On psychometric chart, the constant wet bulb temperature lines coincide with

a)

Constant relative humidity lines

b)

Constant enthalpy lines

c)

Constant dew point temperature lines

d)

Constant volume lines

Q1.10

One ton of refrigeration in kW is equivalent to

a)

1

b)

2.5

c)

210

d)

3.5

Q.2 Solve both questions :

Q2.1

If a gas of volume 6000 cm³ and at pressure of 100 kPa is compressed quasistatically according to $ pV^{2} = \text{constant} $ until the volume becomes 2000 cm³, determine the final pressure and the work transfer.

Q2.2

unavailabile question

Q.3 Solve this question :

Q3.1

A turbine operates under steady flow conditions, receiving steam at the following State: Pressure 1.2 MPa, temperature $ 188^{\circ}C $, enthalpy $ 2785 \text{ kJ/kg} $, velocity $ 333 \text{ m/s} $ and elevation 3 m. The steam leaves the turbine at the following state: Pressure 20 kPa, enthalpy $ 2512 \text{ kJ/kg} $, velocity $ 100 \text{ m/s} $ and elevation 0 m. Heat is lost to the surroundings at the rate of $ 0.20 \text{ kJ/s} $. If the rate of steam flow through the turbine is $ 0.42 \text{ kg/s} $, what is the power output of the turbine in kW?

Q3.2

Prove the equivalence of Clausius statement to the Kelvin Planck statement with schematic diagram.

Q.4 Solve both questions :

Q4.1

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 $ 421^{\circ}C $ from a hot source, while engine B is in communication with a cold sink at a temperature of $ 44^{\circ}C $. If work output of A is twice that of B, find
(i) The intermediate temperature between A and B.
(ii) The efficiency of each engine.
(iii) The heat rejected to the cold sink.

Q4.2

Derive an expression for the efficiency of a Carnot cycle. What is the difficulty in constructing an engine working on Carnot cycle.

Q.5 Solve both questions :

Q5.1

With the help of net sketch, differentiate between the working of Otto and Diesel cycle.

Q5.2

What do you understand by exergy and energy? In a steam generator, water is evaporated at $ 260^{\circ}C $, while the combustion gas $ (c_{p}=1.08 \text{ kJ/kg K}) $ is cooled from $ 1300^{\circ}C $ to $ 320^{\circ}C $. The surroundings are at $ 30^{\circ}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}C = 1662.5 \text{ kJ/kg} $).

Q.6 Solve both questions :

Q6.1

A rigid closed tank of volume contains 5 kg of wet steam at a pressure of 200 kPa. The tank is heated until the steam becomes dry saturated. Determine the final pressure and the heat transfer to the tank.

Q6.2

(i) Write down the van der Waal's equation of state. How does it differ from the ideal gas equation?
(ii) Write three Maxwell's equations.

Q.7 Solve this question :

Q7.1

A geothermal 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}C $. The steam leaves the turbine at 100 mm Hg 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? Use steam table for required data.

Q.8 Solve both questions :

Q8.1

A Brayton cycle operates with air entering the compressor at 1 bar and $ 25^{\circ}C $. The pressure ratio across the compressor is 3 to 1, and the maximum temperature in the cycle is $ 650^{\circ}C $. Determine the compressor work, turbine work, thermal efficiency and work ratio of the cycle.

Q8.2

Describe with net schematic arrangement, working of a simple vapour compression cycle.

Q.9 Solve all questions :

Q9.1

Define the terms 'unsaturated air' and 'relative humidity'.

Q9.2

With the help of suitable diagram, explain the psychrometric chart.

Q9.3

With help of a suitable diagram, explain the process of cooling and dehumidification.


2023 V4 101407

End Semester Examination - 2023 (Semester-IV)

Time 03 Hours
Full Marks 70
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 of the following (Any seven question only):

Q1.1

Which one of the following is the extensive property of thermodynamic system?

a)

Volume

b)

Pressure

c)

Temperature

d)

Density

Q1.2

Ice kept in a well-insulated thermosflask is an example of which system?

a)

Closed System

b)

Isolated System

c)

Open System

d)

Non-flow adiabatic system

Q1.3

Measurement of temperature is based on which law of thermodynamics?

a)

Zero law of thermodynamics

b)

First law of thermodynamics

c)

Second law of thermodynamics

d)

Third law of thermodynamics

Q1.4

A closed system receives 60 kJ heat but its internal energy decreases by 30 kJ. Then the work done by the system is

a)

90 kJ

b)

30 kJ

c)

-30 kJ

d)

-90 kJ

Q1.5

A reversible engine operates between temperature 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. The value of $ T_{2} $ if work outputs of both the engines are equal is

a)

600 K

b)

625 K

c)

650 K

d)

675 K

Q1.6

For real thermodynamics cycle, which one of the following is correct?

a)

\oint \frac{dQ}{T} &gt; 0

b)

\oint \frac{dQ}{T} &lt; 0

c)

dQT=0\oint \frac{dQ}{T} = 0

d)

ds=0\oint ds = 0

Q1.7

The specific volume of water when heated from $ 0^{\circ}C $

a)

first increases and then decreases

b)

increases steadily

c)

decreases and then increases

d)

decreases steadily

Q1.8

A four-stroke petrol engine theoretically operates on

a)

Otto Cycle

b)

Brayton Cycle

c)

Joule Cycle

d)

Rankine Cycle

Q1.9

On psychometric chart, the constant wet bulb temperature lines coincide with

a)

Constant relative humidity lines

b)

Constant enthalpy lines

c)

Constant dew point temperature lines

d)

Constant volume lines

Q1.10

One ton of refrigeration in kW is equivalent to

a)

1

b)

2.5

c)

210

d)

3.5

Q.2 Solve both questions :

Q2.1

If a gas of volume 6000 cm³ and at pressure of 100 kPa is compressed quasistatically according to $ pV^{2} = \text{constant} $ until the volume becomes 2000 cm³, determine the final pressure and the work transfer.

Q2.2

unavailabile question

Q.3 Solve this question :

Q3.1

A turbine operates under steady flow conditions, receiving steam at the following State: Pressure 1.2 MPa, temperature $ 188^{\circ}C $, enthalpy $ 2785 \text{ kJ/kg} $, velocity $ 333 \text{ m/s} $ and elevation 3 m. The steam leaves the turbine at the following state: Pressure 20 kPa, enthalpy $ 2512 \text{ kJ/kg} $, velocity $ 100 \text{ m/s} $ and elevation 0 m. Heat is lost to the surroundings at the rate of $ 0.20 \text{ kJ/s} $. If the rate of steam flow through the turbine is $ 0.42 \text{ kg/s} $, what is the power output of the turbine in kW?

Q3.2

Prove the equivalence of Clausius statement to the Kelvin Planck statement with schematic diagram.

Q.4 Solve both questions :

Q4.1

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 $ 421^{\circ}C $ from a hot source, while engine B is in communication with a cold sink at a temperature of $ 44^{\circ}C $. If work output of A is twice that of B, find
(i) The intermediate temperature between A and B.
(ii) The efficiency of each engine.
(iii) The heat rejected to the cold sink.

Q4.2

Derive an expression for the efficiency of a Carnot cycle. What is the difficulty in constructing an engine working on Carnot cycle.

Q.5 Solve both questions :

Q5.1

With the help of net sketch, differentiate between the working of Otto and Diesel cycle.

Q5.2

What do you understand by exergy and energy? In a steam generator, water is evaporated at $ 260^{\circ}C $, while the combustion gas $ (c_{p}=1.08 \text{ kJ/kg K}) $ is cooled from $ 1300^{\circ}C $ to $ 320^{\circ}C $. The surroundings are at $ 30^{\circ}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}C = 1662.5 \text{ kJ/kg} $).

Q.6 Solve both questions :

Q6.1

A rigid closed tank of volume contains 5 kg of wet steam at a pressure of 200 kPa. The tank is heated until the steam becomes dry saturated. Determine the final pressure and the heat transfer to the tank.

Q6.2

(i) Write down the van der Waal's equation of state. How does it differ from the ideal gas equation?
(ii) Write three Maxwell's equations.

Q.7 Solve this question :

Q7.1

A geothermal 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}C $. The steam leaves the turbine at 100 mm Hg 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? Use steam table for required data.

Q.8 Solve both questions :

Q8.1

A Brayton cycle operates with air entering the compressor at 1 bar and $ 25^{\circ}C $. The pressure ratio across the compressor is 3 to 1, and the maximum temperature in the cycle is $ 650^{\circ}C $. Determine the compressor work, turbine work, thermal efficiency and work ratio of the cycle.

Q8.2

Describe with net schematic arrangement, working of a simple vapour compression cycle.

Q.9 Solve all questions :

Q9.1

Define the terms 'unsaturated air' and 'relative humidity'.

Q9.2

With the help of suitable diagram, explain the psychrometric chart.

Q9.3

With help of a suitable diagram, explain the process of cooling and dehumidification.


2022 101407

B.Tech 4th Semester Exam., 2022 (New Course)

Time 03 Hours
Full Marks 70
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 of the following (any seven):

Q1.1

Extensive property of a system is one whose value

a)

depends on the mass of the system, like volume

b)

does not depend on the mass of the system, like temperature, pressure, etc.

c)

is not dependent on the path followed but on the state

d)

is dependent on the path followed and not on the state

Q1.2

For reversible adiabatic process, the change in entropy is

a)

maximum

b)

minimum

c)

zero

d)

unpredictable

Q1.3

If $ Q_{1} $ is the heat transfer between hot temperature source and machine, and $ Q_{2} $ between cold temperature source and machine, then for heat pump, COP will be equal to

a)

Q1Q1Q2\frac{Q_{1}}{Q_{1}-Q_{2}}

b)

Q2Q1Q2\frac{Q_{2}}{Q_{1}-Q_{2}}

c)

Q1Q2Q1\frac{Q_{1}}{Q_{2}-Q_{1}}

d)

Q2Q2Q1\frac{Q_{2}}{Q_{2}-Q_{1}}

Q1.4

Kelvin-Planck law deals with

a)

conservation of heat

b)

conservation of work

c)

conservation of heat into work

d)

conservation of work into heat

Q1.5

For same compression ratio and for same heat added

a)

Otto cycle is more efficient than diesel cycle

b)

diesel cycle is more efficient than Otto cycle

c)

efficiency depends on other factors

d)

both Otto and diesel cycles are equally efficient

Q1.6

Gas turbine cycle consists of

a)

two isothermal and two isentropic processes

b)

two isentropic and two constant volume processes

c)

two isentropic, one constant volume and one constant pressure processes

d)

two isentropic and two constant pressure processes

Q1.7

Tripple point temperature and pressure for water are

a)

001C0\cdot01^{\circ}C and 0.006028 atm

b)

0C0^{\circ}C and 1 atm

c)

100C100^{\circ}C and 1 atm

d)

1C1^{\circ}C and 1 atm

Q1.8

Select the correct relation.

a)

TdS=dU+pdVTdS = dU + pdV

b)

dH=TdS+VdpdH = TdS + Vdp

c)

TdS=cpdTVdpTdS = c_{p}dT - Vdp

d)

All of the above

Q1.9

The first law of thermodynamics gives $ dU = \delta Q - \delta W $ and the second law tells that $ dS > \frac{\delta Q}{T} $. In which of the way these two laws can be combined and written?

a)

dUTdSpdVdU \ge TdS - pdV

b)

dUdSpdVdU \le dS - pdV

c)

dUTdS+pdVdU \le TdS + pdV

d)

dU=TdSpdVdU = TdS - pdV

Q1.10

Air-standard efficiency of diesel cycle is a function of

a)

compression ratio and the ratio of maximum to minimum temperature

b)

compression ratio and cut-off ratio

c)

compression ratio and the ratio of maximum to minimum pressure

d)

compression ratio and the ratio of exhaust temperature to inlet temperature

Q.2 Define the following terms:

Q2.1

(a) Perpetual motion machine of second kind
(b) Point and path functions
(c) Total energy of the system
(d) Psychrometry
(e) Pure substance
(f) Exergy destruction
(g) Refrigeration

Q.3 Solve both questions :

Q3.1

A certain water heater operates under steady flow conditions receiving $ 4.2 \text{ kg/s} $ of water at $ 75^{\circ}C $ temperature, enthalpy $ 313\cdot93 \text{ kJ/kg} $. The water is heated by mixing with the steam which is supplied to the heater at temperature $ 100\cdot2^{\circ}C $ and enthalpy $ 2676 \text{ kJ/kg} $. The mixture leaves the heater as liquid water at temperature $ 100^{\circ}C $ and enthalpy $ 419 \text{ kJ/kg} $. How much steam must be supplied to the heater per hour?

Q3.2

In an air-standard diesel cycle, the compression ratio is 16, and at the beginning of isentropic compression, the temperature is $ 15^{\circ}C $ and the pressure is 0.1 MPa. Heat is added until the temperature at the end of the constant pressure process is $ 1480^{\circ}C $. Calculate (i) the cut-off ratio, (ii) the heat supplied per kg of air, (iii) the cycle efficiency, and (iv) the mean effective pressure.

Q.4 Solve both questions :

Q4.1

A gas flows steadily through a rotary compressor. The gas enters the compressor at a temperature of $ 16^{\circ}C $, a pressure of 100 kPa, and an enthalpy of $ 391\cdot2 \text{ kJ/kg} $. The gas leaves the compressor at a temperature of $ 245^{\circ}C $, a pressure of 0.6 MPa, and enthalpy of $ 534\cdot5 \text{ kJ/kg} $. There is no heat transfer to or from the gas as it flows through the compressor. Evaluate the external work done per unit mass of gas assuming the gas velocities at entry and exit to be negligible.

Q4.2

Evaluate the external work done per unit mass of gas when the gas velocity at entry is $ 80 \text{ m/s} $ and that at exit is $ 160 \text{ m/s} $.

Q.5 Solve both questions :

Q5.1

Define 'reversibility' and 'irreversibility'. What are the various causes of irreversibility?

Q5.2

Derive an expression for entropy change in an irreversible process.

Q.6 Solve both questions :

Q6.1

State Kelvin-Planck and Clausius statements for 2nd law of thermodynamics and show the equivalence between these statements.

Q6.2

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\cdot20 \text{ m}^{3} $ and $ 1\cdot20 \text{ m}^{3} $. The specific internal energy of the gas is given by the relation $ u = 1.5 pv - 85 \text{ kJ/kg} $, where p is in kPa and v is in $ \text{m}^{3}\text{/kg} $. Calculate the net transfer and maximum internal energy of the gas attained during expansion.

Q.7 Solve this question :

Q7.1

Saturated air at $ 2^{\circ}C $ is required to be supplied to a room where the temperature must be held at $ 20^{\circ}C $ with a relative humidity of 50%. The air is heated and then water at $ 10^{\circ}C $ is sprayed in to give the required humidity. Determine the temperature to which the air must be heated and the mass of spray water required per $ \text{m}^{3} $ of air at room conditions. Assume that the total pressure is constant at 1.013 bar and neglect the fan power. Use steam table for required data.

Q.8 Solve both questions :

Q8.1

What are Helmholtz's and Gibbs' functions? Write four Maxwell's equations.

Q8.2

A turbo-compressor delivers $ 2\cdot33 \text{ m}^{3}\text{/s} $ of air at 0.276 MPa, $ 43^{\circ}C $ which is heated at this pressure to $ 430^{\circ}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 energies are negligible.

Q.9 Solve both questions :

Q9.1

A vessel of volume $ 0.04 \text{ 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.
Given: At $ 250^{\circ}C $, $ P_{sat} = 3\cdot973 \text{ MPa} $, $ \nu_{f} = 0.0012512 \text{ m}^{3}\text{/kg} $, $ \nu_{g} = 0.05013 \text{ m}^{3}\text{/kg} $, $ h_{f} = 1085\cdot36 \text{ kJ/kg} $, $ h_{fg} = 1716\cdot2 \text{ kJ/kg} $, $ s_{f} = 2\cdot7927 \text{ kJ/kg K} $, $ s_{fg} = 3\cdot2802 \text{ kJ/kg K} $, $ u_{f} = 1080\cdot39 \text{ kJ/kg} $, $ u_{fg} = 1522 \text{ kJ/kg} $.

Q9.2

A gas turbine plant operates on the Brayton cycle between the temperatures $ 27^{\circ}C $ and $ 800^{\circ}C $.
(i) Find the pressure ratio at which the cycle efficiency approaches the Carnot cycle efficiency.
(ii) Find the pressure ratio at which the work done per kg of air is maximum.
(iii) Compare the efficiency at this pressure ratio with the Carnot efficiency for the given temperatures.


2022 V4 101407

B.Tech 4th Semester Exam., 2022 (New Course)

Time 03 Hours
Full Marks 70
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 of the following (any seven):

Q1.1

Extensive property of a system is one whose value

a)

depends on the mass of the system, like volume

b)

does not depend on the mass of the system, like temperature, pressure, etc.

c)

is not dependent on the path followed but on the state

d)

is dependent on the path followed and not on the state

Q1.2

For reversible adiabatic process, the change in entropy is

a)

maximum

b)

minimum

c)

zero

d)

unpredictable

Q1.3

If $ Q_{1} $ is the heat transfer between hot temperature source and machine, and $ Q_{2} $ between cold temperature source and machine, then for heat pump, COP will be equal to

a)

Q1Q1Q2\frac{Q_{1}}{Q_{1}-Q_{2}}

b)

Q2Q1Q2\frac{Q_{2}}{Q_{1}-Q_{2}}

c)

Q1Q2Q1\frac{Q_{1}}{Q_{2}-Q_{1}}

d)

Q2Q2Q1\frac{Q_{2}}{Q_{2}-Q_{1}}

Q1.4

Kelvin-Planck law deals with

a)

conservation of heat

b)

conservation of work

c)

conservation of heat into work

d)

conservation of work into heat

Q1.5

For same compression ratio and for same heat added

a)

Otto cycle is more efficient than diesel cycle

b)

diesel cycle is more efficient than Otto cycle

c)

efficiency depends on other factors

d)

both Otto and diesel cycles are equally efficient

Q1.6

Gas turbine cycle consists of

a)

two isothermal and two isentropic processes

b)

two isentropic and two constant volume processes

c)

two isentropic, one constant volume and one constant pressure processes

d)

two isentropic and two constant pressure processes

Q1.7

Tripple point temperature and pressure for water are

a)

001C0\cdot01^{\circ}C and 0.006028 atm

b)

0C0^{\circ}C and 1 atm

c)

100C100^{\circ}C and 1 atm

d)

1C1^{\circ}C and 1 atm

Q1.8

Select the correct relation.

a)

TdS=dU+pdVTdS = dU + pdV

b)

dH=TdS+VdpdH = TdS + Vdp

c)

TdS=cpdTVdpTdS = c_{p}dT - Vdp

d)

All of the above

Q1.9

The first law of thermodynamics gives $ dU = \delta Q - \delta W $ and the second law tells that $ dS > \frac{\delta Q}{T} $. In which of the way these two laws can be combined and written?

a)

dUTdSpdVdU \ge TdS - pdV

b)

dUdSpdVdU \le dS - pdV

c)

dUTdS+pdVdU \le TdS + pdV

d)

dU=TdSpdVdU = TdS - pdV

Q1.10

Air-standard efficiency of diesel cycle is a function of

a)

compression ratio and the ratio of maximum to minimum temperature

b)

compression ratio and cut-off ratio

c)

compression ratio and the ratio of maximum to minimum pressure

d)

compression ratio and the ratio of exhaust temperature to inlet temperature

Q.2 Define the following terms:

Q2.1

(a) Perpetual motion machine of second kind
(b) Point and path functions
(c) Total energy of the system
(d) Psychrometry
(e) Pure substance
(f) Exergy destruction
(g) Refrigeration

Q.3 Solve both questions :

Q3.1

A certain water heater operates under steady flow conditions receiving $ 4.2 \text{ kg/s} $ of water at $ 75^{\circ}C $ temperature, enthalpy $ 313\cdot93 \text{ kJ/kg} $. The water is heated by mixing with the steam which is supplied to the heater at temperature $ 100\cdot2^{\circ}C $ and enthalpy $ 2676 \text{ kJ/kg} $. The mixture leaves the heater as liquid water at temperature $ 100^{\circ}C $ and enthalpy $ 419 \text{ kJ/kg} $. How much steam must be supplied to the heater per hour?

Q3.2

In an air-standard diesel cycle, the compression ratio is 16, and at the beginning of isentropic compression, the temperature is $ 15^{\circ}C $ and the pressure is 0.1 MPa. Heat is added until the temperature at the end of the constant pressure process is $ 1480^{\circ}C $. Calculate (i) the cut-off ratio, (ii) the heat supplied per kg of air, (iii) the cycle efficiency, and (iv) the mean effective pressure.

Q.4 Solve both questions :

Q4.1

A gas flows steadily through a rotary compressor. The gas enters the compressor at a temperature of $ 16^{\circ}C $, a pressure of 100 kPa, and an enthalpy of $ 391\cdot2 \text{ kJ/kg} $. The gas leaves the compressor at a temperature of $ 245^{\circ}C $, a pressure of 0.6 MPa, and enthalpy of $ 534\cdot5 \text{ kJ/kg} $. There is no heat transfer to or from the gas as it flows through the compressor. Evaluate the external work done per unit mass of gas assuming the gas velocities at entry and exit to be negligible.

Q4.2

Evaluate the external work done per unit mass of gas when the gas velocity at entry is $ 80 \text{ m/s} $ and that at exit is $ 160 \text{ m/s} $.

Q.5 Solve both questions :

Q5.1

Define 'reversibility' and 'irreversibility'. What are the various causes of irreversibility?

Q5.2

Derive an expression for entropy change in an irreversible process.

Q.6 Solve both questions :

Q6.1

State Kelvin-Planck and Clausius statements for 2nd law of thermodynamics and show the equivalence between these statements.

Q6.2

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\cdot20 \text{ m}^{3} $ and $ 1\cdot20 \text{ m}^{3} $. The specific internal energy of the gas is given by the relation $ u = 1.5 pv - 85 \text{ kJ/kg} $, where p is in kPa and v is in $ \text{m}^{3}\text{/kg} $. Calculate the net transfer and maximum internal energy of the gas attained during expansion.

Q.7 Solve this question :

Q7.1

Saturated air at $ 2^{\circ}C $ is required to be supplied to a room where the temperature must be held at $ 20^{\circ}C $ with a relative humidity of 50%. The air is heated and then water at $ 10^{\circ}C $ is sprayed in to give the required humidity. Determine the temperature to which the air must be heated and the mass of spray water required per $ \text{m}^{3} $ of air at room conditions. Assume that the total pressure is constant at 1.013 bar and neglect the fan power. Use steam table for required data.

Q.8 Solve both questions :

Q8.1

What are Helmholtz's and Gibbs' functions? Write four Maxwell's equations.

Q8.2

A turbo-compressor delivers $ 2\cdot33 \text{ m}^{3}\text{/s} $ of air at 0.276 MPa, $ 43^{\circ}C $ which is heated at this pressure to $ 430^{\circ}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 energies are negligible.

Q.9 Solve both questions :

Q9.1

A vessel of volume $ 0.04 \text{ 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.
Given: At $ 250^{\circ}C $, $ P_{sat} = 3\cdot973 \text{ MPa} $, $ \nu_{f} = 0.0012512 \text{ m}^{3}\text{/kg} $, $ \nu_{g} = 0.05013 \text{ m}^{3}\text{/kg} $, $ h_{f} = 1085\cdot36 \text{ kJ/kg} $, $ h_{fg} = 1716\cdot2 \text{ kJ/kg} $, $ s_{f} = 2\cdot7927 \text{ kJ/kg K} $, $ s_{fg} = 3\cdot2802 \text{ kJ/kg K} $, $ u_{f} = 1080\cdot39 \text{ kJ/kg} $, $ u_{fg} = 1522 \text{ kJ/kg} $.

Q9.2

A gas turbine plant operates on the Brayton cycle between the temperatures $ 27^{\circ}C $ and $ 800^{\circ}C $.
(i) Find the pressure ratio at which the cycle efficiency approaches the Carnot cycle efficiency.
(ii) Find the pressure ratio at which the work done per kg of air is maximum.
(iii) Compare the efficiency at this pressure ratio with the Carnot efficiency for the given temperatures.


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