Thermodynamics (XE-E) - GATE XE (Engineering Sciences) Subject-Wise PYQ Practice

Question 1

A tank is divided into two compartments with one compartment containing a gas at a given pressure, while the second is completely evacuated. If the partition is removed, the gas occupies the entire compartment. Which one of the following statements is CORRECT?

Accepted Answer

Expansion of gas is not restrained by external force

Answer

Work done is equal to the area under the curve of a p V − diagram

Answer

The entire process is reversible

Answer

The overall change in volume is zero for the entire system

Question 2

A cylinder of volume 0.1 m3 is filled with nitrogen at 10 MPa and 300 K. Consider nitrogen to be an ideal gas. The cylinder develops a leak and nitrogen escapes to atmosphere which is at 0.1 MPa. After sometime, the pressure in the cylinder reduces to 5 MPa. Assuming the cylinder and the leaked gas temperature remains constant at 300 K, the work done (in MJ) by nitrogen gas is

Accepted Answer

0.5

Answer

0.1

Answer

1

Answer

10

Question 3

A closed system undergoes a process 1–2 in which it absorbs 150 kJ of energy as heat and does 90 kJ of work. Then it follows another process 2–3 in which 80 kJ of work is done on it while it rejects 60 kJ as heat. If it is desired to restore the system to the initial state (state 1) by an adiabatic path, the work interaction (in kJ) in this process will be

Accepted Answer

80

Answer

100

Answer

50

Answer

70

Question 4

The inlet and outlet temperatures of the flowing fluid during a steady state flow process are the same as that of the surroundings. If the changes in kinetic and potential energies are neglected, the maximum power that can be obtained is equal to

Accepted Answer

the rate of decrease in Gibbs free energy of the flowing fluid

Answer

the rate of increase in enthalpy of the flowing fluid

Answer

the rate of decrease in Helmholtz energy of the flowing fluid

Answer

the rate of decrease in internal energy of the flowing fluid

Question 5

If 𝛾 refers to the ratio of specific heats, the air-standard efficiency of an Otto cycle is

Accepted Answer

1 − 1 (Compression ratio)(𝛾−1)

Answer

1 − 1 (Compression ratio)𝛾

Answer

1 − 1 (Pressure ratio) (𝛾−1 𝛾)

Answer

1 − 1 (Pressure ratio)(𝛾−1)

Question 6

Let 𝑇𝐻 and 𝑇𝐿 denote the absolute temperatures of high and low temperature reservoirs, respectively. The coefficient of performance of a reversible refrigerator operating between these two reservoirs is

Accepted Answer

1 𝑇𝐻 𝑇𝐿−1

Answer

1 1 −𝑇𝐻 𝑇𝐿

Answer

1 𝑇𝐿 𝑇𝐻−1

Answer

1 𝑇𝐿 𝑇𝐻+ 1

Question 7

A tank of 4 m3 contains an ideal gas mixture of 60% hydrogen and 40% nitrogen by volume at 100 kPa and 300 K. Nitrogen is added to the tank such that the composition changes to 50% nitrogen by volume, with a final temperature of 300 K. The amount of nitrogen (in kmol) to be added is ___________ (rounded off to three decimal places). Use: Universal gas constant (Ru) = 8.314 kJ/kmol-K

Accepted Answer

0.030 to 0.034

Question 8

A heat engine having thermal efficiency of 40% receives heat from a source at 600 K and rejects heat to a sink at 300 K. The second-law efficiency (in %) of this engine is ___________ (answer in integer).

Accepted Answer

80

Question 9

A rigid tank of 300 litre capacity contains 3 kg of oxygen (molar mass = 32 kg/kmol) at 25 °C. If oxygen behaves as an ideal gas, the pressure (in kPa) inside the tank is _______________ (rounded off to two decimal places). Use: Universal gas constant (Ru) = 8.314 kJ/kmol-K

Accepted Answer

773 to 776

Question 10

For an ideal gas turbine cycle, 𝑇1 and 𝑇3 are the compressor inlet temperature and turbine inlet temperature respectively. The ratio 𝑇3 𝑇1 is denoted by 𝑡 and the ratio of specific heats is denoted by 𝛾. For any given 𝑡, the optimum pressure ratio for the maximum specific work output is

Accepted Answer

𝑡 𝛾 2(𝛾−1)

Answer

𝑡 2 (𝛾−1)

Answer

𝑡 𝛾 (𝛾−1)

Answer

𝑡 𝛾−1 𝛾

Question 11

For a pure substance that expands on freezing, which of the following statement(s) is/are CORRECT?

Accepted Answer

Temperature of the liquid phase can be lower than the temperature at the triple point

Accepted Answer

Highest temperature at which solid-liquid phase change can happen is the temperature at the triple point

Answer

Critical pressure is equal to the pressure at the triple point

Answer

Highest pressure at which the vapour phase can exist is the pressure at the triple point

Question 12

Consider a gas obeying the relation ( ) P v b RT − = , where b and R are constants. Which of the following statement(s) is/are CORRECT about the specific heat capacity at constant pressure?

Accepted Answer

It is a function of temperature

Accepted Answer

It is independent of both specific volume and pressure

Answer

It is independent of temperature

Answer

It is a function of pressure

Question 13

A piston-cylinder arrangement contains an ideal gas mixture of 4 kg of hydrogen and 13 kg of nitrogen at 250 K and atmospheric pressure. On heat addition, the mixture expands at constant pressure until the temperature rises to 350 K. The average isobaric specific heats (𝑐𝑝) for hydrogen and nitrogen are 14.239 kJ/kg-K and 1.040 kJ/kg-K, respectively. The amount of heat (in MJ) added to the cylinder is _________________ (rounded off to three decimal places).

Accepted Answer

6.9 to 7.2

Question 14

Air in an ideal Diesel cycle is compressed from 3 litre to 0.15 litre. It then expands during a constant pressure heat addition process to 0.3 litre. If the ratio of specific heats, γ = 1.4, the thermal efficiency (in %) of the cycle is ___________ (rounded to one decimal place).

Accepted Answer

63 to 66

Question 15

Air at 101 kPa, 15 °C and 50% relative humidity is first heated to 20 °C in a heating coil, and then humidified by spraying water on it. In the final state, the air has temperature of 25 °C and relative humidity of 85%. The amount of water sprayed (in gm per kg of dry air) is _______________ (rounded off to two decimal places). Use the following data: The saturation pressure of water at 15 °C = 1.7057 kPa The saturation pressure of water at 25 °C = 3.1698 kPa

Accepted Answer

11.5 to 12.0

Question 16

A stream of superheated steam (2 MPa, 300 °C) mixes with another stream of superheated steam (2 MPa, 400 °C) through a steady-state adiabatic process. The flow rates of the streams are 3 kg/min and 2 kg/min, respectively. This mixture then expands in an adiabatic nozzle to a saturated mixture with quality of 0.77 and 1 kPa. Neglect the velocity at the nozzle entrance and the change in potential energies. The velocity at the nozzle exit (in m/s) is ___________ (rounded off to two decimal places). Use the following data: At 2 MPa, 300 °C: Specific enthalpy of superheated steam = 3024.2 kJ/kg At 2 MPa, 400 °C: Specific enthalpy of superheated steam = 3248.4 kJ/kg At 1 kPa: Specific enthalpy of saturated water = 29.3 kJ/kg At 1 kPa: Specific enthalpy of saturated vapour = 2513.7 kJ/kg

Accepted Answer

1515 to 1545

Question 17

A piston-cylinder assembly having 250 mm diameter contains 0.01 kg of water vapor at 1 MPa and 200 °C. The specific volume of the vapor is 0.20602 m3/kg. The system expands as per the relation 𝑝𝑉𝑛 = constant, where p is pressure and V is volume. The expansion of water vapour displaces the piston by 50 mm. If the final pressure is 0.35 MPa, the value of the exponent (𝑛) is __________ (rounded off to two decimal places).

Accepted Answer

1.30 to 1.38

Question 18

Air enters a hair dryer at 22 °C and 100 kPa with a velocity of 3.7 m/s, and leaves the dryer at 83 °C and 100 kPa with a velocity of 9.1 m/s. The exit area of the dryer is 18.7 cm2, and the ambient temperature is 22 °C. The air is an ideal gas with gas constant 𝑅 = 0.287 kJ/kg-K and isobaric specific heat 𝑐𝑝 = 1.005 kJ/kg-K. If the change in potential energy is neglected, the second law efficiency (in %) of the dryer is __________ (rounded off to one decimal place).

Accepted Answer

8.9 to 9.4

Question 19

A steam boiler contains saturated water vapour at 200 °C. After a certain period, the temperature of the boiler drops to 110 °C. Assume that all the valves of the boiler are closed and the energy is lost as heat to the surroundings. The ratio of mass of liquid to the mass of vapour is ___________ (rounded off to two decimal places). Saturated volume of vapour phase at 200 °C = 0.127 m3/kg Saturated volume of vapour phase at 110 °C = 1.210 m3/kg Saturated volume of liquid phase at 110 °C = 0.001 m3/kg

Accepted Answer

8.1 to 8.9

Question 20

Two Carnot heat engines (E1 and E2) are operating in series as shown in figure. Engine E1 receives heat from a reservoir at 𝑇𝐻 = 1600 K and does work W1. Engine E2 receives heat from an intermediate reservoir at T, does work W2 and rejects the rest to a reservoir at 𝑇𝐿 = 400 K. Both the engines have identical thermal efficiencies. The temperature T (in K) of the intermediate reservoir is __________ (answer in integer). T = ? TH TL W1 W2 E1 E2

Accepted Answer

800

Question 21

A particular temperature scale is obtained according to the relation: t ae b α = + where a and b are constants, and t is in °C. The thermometric property as measured by the thermometer is α. The values of α at ice point and steam point are 6 and 9, respectively. The temperature (in °C) which gives α = 7 is __________ (rounded off to two decimal places).

Accepted Answer

8.9 to 9.1

Question 22

In a piston cylinder assembly, one kmol of an ideal gas is compressed from an initial state of 200 kPa and 400 K to a final state of 1 MPa and 400 K. If the surroundings are at 400 K, the minimum amount of work (in kJ/kmol) required for the compression process is ______________ (rounded off to two decimal places). Use: Universal gas constant (Ru) = 8.314 kJ/kmol-K

Accepted Answer

5300 to 5400

Question 23

A heat source at temperature 𝑇𝐻 transfers the same amount of heat to a sink under the following situations: Case A: Sink is at temperature 𝑇𝐿,1 Case B: Sink is at temperature 𝑇𝐿,2 If 𝑇𝐿,1 <⁡𝑇𝐿,2, which one of the following statements is TRUE?

Accepted Answer

Case B is more reversible with the entropy generation greater than zero

Answer

The reversibility is the same, and the entropy generation is greater than zero for Cases A and B

Answer

Case B is less reversible with the entropy generation greater than zero

Answer

Case B is more reversible with the entropy generation equal to zero

Question 24

Given 𝑣 is the molar specific volume, 𝑃 is the pressure, 𝑇 is the temperature, 𝑅 is the Universal gas constant, and 𝑎, 𝑏 are van der Waal’s constants. The van der Waal’s equation of state is 𝑃= 𝑅𝑇 𝑣−𝑏−𝑎 𝑣2 The value of ( 𝜕𝑣 𝜕𝑇) 𝑃( 𝜕𝑃 𝜕𝑣) 𝑇( 𝜕𝑇 𝜕𝑃) 𝑣 is

Accepted Answer

−1

Answer

𝑎 𝑏2

Answer

1

Answer

𝑏2 𝑎

Question 25

The temperature of 10⁡g of liquid water (𝑐𝑝= 4.2⁡J/g.K) in an insulated container is raised by 5⁡K by stirring. The amount of heat transferred to the water (in J) is

Accepted Answer

0

Answer

210

Answer

420

Answer

105

Question 26

The figure shows four different processes labeled 1, 2, 3, and 4 for the same closed system containing an ideal gas. The curves labeled 𝑇1, 𝑇2, and 𝑇3 are isotherms. For which one of the these four processes, the magnitude of internal energy change is the highest?

Accepted Answer

Process 1

Answer

Process 2

Answer

Process 3

Answer

Process 4

Question 27

A power plant operates on a simple ideal Rankine cycle. If superheating is added to this cycle, then which one of the following options is CORRECT ?

Accepted Answer

Pump work remains same, turbine work output increases, cycle efficiency increases, and moisture content at turbine exit decreases

Answer

Pump work increases, turbine work output increases, cycle efficiency increases, and moisture content at turbine exit increases

Answer

Pump work remains same, turbine work output increases, cycle efficiency increases, and moisture content at turbine exit increases

Answer

Pump work decreases, turbine work output increases, cycle efficiency increases, and moisture content at turbine exit decreases

Question 28

Consider a mixture of ideal gases with total pressure, volume, and temperature as 𝑃, 𝑉, and 𝑇, respectively. The partial pressure, number of moles, and temperature of each component “𝑖” of the mixture are 𝑃𝑖 , 𝑁𝑖 , and 𝑇𝑖 , respectively. Which of the following statements is/are TRUE ?

Accepted Answer

𝑇= ∑𝑇𝑖 𝑖

Answer

𝑃= ∑𝑃𝑖 𝑖

Answer

𝑉= ∑𝑁𝑖𝑅𝑇 𝑃 𝑖

Answer

𝑉= ∑𝑁𝑖𝑅𝑇 𝑃𝑖 𝑖

Question 29

Two rigid, impermeable containers 𝐴 and 𝐵 are filled with an ideal gas. They are allowed to exchange heat only with each other and not with the surroundings. 𝑃, 𝑉, 𝑁, and 𝑇 represent the pressure, total volume, number of moles, and temperature, respectively. At equilibrium, which of the following conditions is/are necessarily satisfied? (Subscripts 𝐴 and 𝐵 represent properties of the gas in the respective containers.)

Accepted Answer

𝑇𝐴= 𝑇𝐵

Accepted Answer

𝑃𝐴𝑉𝐴 𝑁𝐴 = 𝑃𝐵𝑉𝐵 𝑁𝐵

Answer

𝑃𝐴= 𝑃𝐵

Answer

𝑃𝐴 𝑉𝐴 = 𝑃𝐵 𝑉𝐵

Question 30

Following data is for an actual vapour compression refrigeration cycle. Enthalpy at compressor inlet: 246⁡kJ/kg Enthalpy at compressor exit: 286⁡kJ/kg Heat load on the evaporator: 158⁡kJ/kg The enthalpy at the exit of the condenser in kJ/kg is ________ (rounded off to the nearest integer).

Accepted Answer

88

Question 31

A rigid tank, initially at 1⁡bar and⁡300⁡K, contains 5⁡moles of 𝑂2, 4⁡moles of 𝑁2 , and 3⁡moles of 𝐻2 . From this tank, 2⁡moles of 𝑂2 are removed keeping the temperature constant. Assuming ideal gas behaviour, the final partial pressure of 𝑂2 (in bar) inside the tank is _______ (rounded off to three decimal places). Use 𝑅⁡ = ⁡8.314⁡J/mol.K Molecular weights of 𝐻2, 𝑁2 and 𝑂2 are 2⁡g/mol, 28⁡g/mol, and 32⁡g/mol respectively.

Accepted Answer

0.249 to 0.251

Question 32

A fixed mass of an ideal gas undergoes two different cycles M and N as shown in the Pressure (𝑃) – Volume (𝑉) diagrams. Based on the information provided, which one of the following statements is always TRUE ?

Accepted Answer

Net heat transfer in Cycle M is equal to net heat transfer in Cycle N

Answer

Heat input in Cycle M is equal to heat input in Cycle N

Answer

Heat rejected in Cycle M is equal to heat rejected in Cycle N

Answer

Thermal efficiency of Cycle M is equal to thermal efficiency of Cycle N

Question 33

In a graph with Helmholtz function on the 𝑦–axis and volume on the 𝑥–axis, the slope of the isothermal curves for a finite volume system containing an ideal gas is

Accepted Answer

finite, negative, and non-zero

Answer

always zero

Answer

infinite

Answer

finite, positive, and non-zero

Question 34

Match each quantity in Column M with the appropriate relation from Column N. Here, 𝜓 is Helmholtz function, 𝑃 is pressure, 𝑣 is specific volume, 𝑇 is temperature, ℎ is specific enthalpy, and 𝑠 is specific entropy. Column M Column N (M1)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑣 (M2)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑃 (M3)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑠 (M4)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝑇 (N1)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡−⁡𝜕𝜓 𝜕𝑣| 𝑇 (N2)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ 𝜕𝜓 𝜕𝑣| 𝑇 (N3)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ 𝜕𝜓 𝜕𝑇| 𝑣 (N4)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡−⁡ 𝜕𝜓 𝜕𝑇| 𝑣 (N5)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡𝜕ℎ 𝜕𝑃| 𝑠 (N6)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡−⁡ 𝜕ℎ 𝜕𝑠| 𝑃 (N7) ⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡− 𝜕ℎ 𝜕𝑃| 𝑠 (N8)⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡⁡ 𝜕ℎ 𝜕𝑠| 𝑃

Accepted Answer

M1-N5, M2-N1, M3-N4, M4-N8

Answer

M1-N5, M2-N1, M3-N4, M4-N7

Answer

M1-N6, M2-N2, M3-N3, M4-N8

Answer

M1-N8, M2-N1, M3-N4, M4-N5

Question 35

10⁡kg of water at 300⁡K is poured into a bucket containing 10⁡kg of water at 350⁡K. Heat capacity of water is 4.2⁡kJ/kg.K . Neglecting any heat losses to the surroundings, the change in the entropy (in kJ/K) of the system during this process (rounded off to two decimal places) is

Accepted Answer

0.25

Answer

0.00

Answer

0.50

Answer

0.75

Question 36

A Carnot engine operates between two temperatures T1 and T2 such that T1 > T2. If the thermal efficiency of the engine is to be increased by changing one of the temperatures by a constant amount ∆T > 0, which one of the following cases will give the highest increase in efficiency?

Accepted Answer

Decreasing T2 by ∆T while keeping T1 constant

Answer

Increasing T1 by ∆T while keeping T2 constant

Answer

Decreasing T1 by ∆T while keeping T2 constant

Answer

Increasing T2 by ∆T while keeping T1 constant

Question 37

The equation of state for a non-ideal gas is 𝑃𝑣 𝑅𝑇= 1 + 𝐵𝑃 where 𝑃 is pressure, 𝑣 is specific volume, 𝑅 is the specific gas constant, 𝑇 is temperature, and 𝐵 is a temperature dependent parameter. For this gas, the partial derivative of enthalpy with respect to pressure at constant temperature is

Accepted Answer

−𝑅𝑇2 (𝑑𝐵 𝑑𝑇)

Answer

𝐵𝑅𝑇

Answer

𝐵𝑅𝑇−𝑅𝑇2 (𝑑𝐵 𝑑𝑇)

Answer

0

Question 38

Consider the following data from a Brayton cycle. Enthalpy at inlet to turbine: 1400⁡kJ/kg Enthalpy at exit of turbine: 880⁡kJ/kg Enthalpy at exit of compressor: 600⁡kJ/kg On adding a regenerator of effectiveness equal to 0.8, the absolute value of percentage change in heat addition is __________ (rounded off to the nearest integer).

Accepted Answer

28

Question 39

An ideal gas undergoes a series of reversible steady state, steady flow processes between states 1, 2, and 3. Process 1→2 satisfies the relation 𝑃+ 800𝑣= 900, where pressure, 𝑃 is in kPa and specific volume, 𝑣 is in m3/kg. Process 2→3 is isochoric. Given that 𝑣1 = 0.5⁡m3/kg, ⁡𝑣2 = 𝑣3 = 1⁡m3/kg,⁡⁡ 𝑃3 𝑃2 = 4, the total work done per unit mass (in kJ/kg) in the series of processes 1→2→3 is _________ (rounded off to the nearest integer).

Accepted Answer

0

Question 40

Air (assumed as an ideal gas) with a mass flow rate of 2.5⁡kg/s enters a horizontal nozzle at 350⁡K, 350⁡kPa with a velocity of 3⁡m/s. The air exits the nozzle at a pressure of 101.5⁡kPa and temperature 305⁡K with a Mach number of 9 7 . Assuming steady state operation and constant properties given in the data, the ratio of inlet area to exit area required to satisfy the exit condition is ___________ (rounded off to one decimal place). Use the following data: 𝛾= 1.4, 𝑐𝑝= 1.011⁡kJ/kg.K, ⁡⁡𝑅= 0.287⁡kJ/kg.K

Accepted Answer

49.0 to 51.0

Question 41

The melting point of a substance at 1⁡bar is 273⁡K. The following property data is available for this substance at 1⁡bar. Density of the solid phase 900⁡kg/m3 Density of the liquid phase 1000⁡kg/m3 Latent heat for melting 300⁡kJ/kg Assuming that the above properties are constant, the melting point (in K) of the substance at 101⁡bar is ________ (rounded off to two decimal places).

Accepted Answer

271.50 to 272.50

Question 42

100⁡moles of moist air at 70% relative humidity is cooled from 70⁡oC to 50⁡oC at a constant pressure of 1⁡bar. The vapour pressures of water are given in the table. The number of moles of water left in the moist air at the end of this process is _________(rounded off to two decimal places). 𝐓𝐞𝐦𝐩𝐞𝐫𝐚𝐭𝐮𝐫𝐞⁡(𝐨𝐂) 𝐕𝐚𝐩𝐨𝐮𝐫⁡𝐏𝐫𝐞𝐬𝐬𝐮𝐫𝐞⁡(𝐤𝐏𝐚) 50 12.34 70 31.16

Accepted Answer

10.50 to 11.50

Question 43

A rigid insulated tank containing an ideal gas at 300 K and 1⁡bar is being filled from an external pressurized line supplying the same gas at 300 K and 10⁡bar. When the mass of gas inside the tank has doubled, its temperature (in K) is _______ (rounded off to the nearest integer). Assume ratio of specific heats to be constant for this process and equal to 1.4.

Accepted Answer

359 to 361

Question 44

A piston-cylinder system contains 2⁡kg of wet steam at 90⁡oC with quality of 0.1 . The piston is loaded with a linear spring. The steam expands to 800⁡kPa and 250⁡oC on heating. The work done (in kJ) in this process is ______ (rounded off to two decimal places). Use the following data: At 90⁡oC: 𝑃𝑠𝑎𝑡= 70⁡kPa, 𝑣𝑓= 0.001⁡m3/kg, 𝑣𝑔= 2.4⁡m3/kg At 250⁡oC and 800⁡kPa: 𝑣⁡ = ⁡0.29⁡m3/kg

Accepted Answer

40.000 to 44.500

Question 45

A The number of properties required to fix the state of a system is given by ‘state postulate’. R The state of a simple compressible system is completely specified by two independent, intensive properties. About the statements A and R applied to a single-phase system,

Accepted Answer

Both A and R are correct.

Answer

A is correct and R is incorrect.

Answer

A is incorrect and R is correct.

Answer

Both A and R are incorrect.

Question 46

Which of the following is an extensive property of a system?

Accepted Answer

Total mass

Answer

Density

Answer

Pressure

Answer

Temperature

Question 47

A tank of volume V contains homogeneous mixture of two ideal gases, A and B at a temperature T and a pressure P. The mixture contains nA moles of gas A and nB moles of gas B. If PA and PB are the partial pressures of gas A and gas B, respectively, then

Accepted Answer

𝑃𝐴= 𝑛𝐴 𝑛𝐴+ 𝑛𝐵 𝑃, 𝑃𝐵= 𝑛𝐵 𝑛𝐴+ 𝑛𝐵 𝑃

Answer

𝑃𝐴= 𝑛𝐵 𝑛𝐴 𝑃, 𝑃𝐵= 𝑛𝐴 𝑛𝐵 𝑃

Answer

𝑃𝐴= 𝑛𝐴 𝑛𝐵 𝑃, 𝑃𝐵= 𝑛𝐵 𝑛𝐴 𝑃

Answer

𝑃𝐴= 𝑛𝐵 𝑛𝐴+ 𝑛𝐵 𝑃, 𝑃𝐵= 𝑛𝐴 𝑛𝐴+ 𝑛𝐵 𝑃

Question 48

If an ideal air-standard Otto cycle and an ideal air-standard Diesel cycle operate on the same compression ratio, then the relation between the thermal efficiencies (ηth) of the cycles is

Accepted Answer

𝜂𝑡ℎ,𝑂𝑡𝑡𝑜> 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙

Answer

𝜂𝑡ℎ,𝑂𝑡𝑡𝑜= 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙 and 𝜂𝑡ℎ,𝑂𝑡𝑡𝑜< 1

Answer

𝜂𝑡ℎ,𝑂𝑡𝑡𝑜< 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙

Answer

𝜂𝑡ℎ,𝑂𝑡𝑡𝑜= 𝜂𝑡ℎ,𝐷𝑖𝑒𝑠𝑒𝑙= 1

Question 49

The following statements are given: (i) The third law of thermodynamics deals with the entropy of a substance at the absolute zero temperature. (ii) Entropy of any non-crystalline structure is zero at absolute zero temperature. (iii) At the absolute zero temperature, the crystal structure has maximum degree of order. (iv) The thermal energy of the substance at absolute zero temperature is maximum. The correct option describing these statements is

Accepted Answer

Both (i) and (iii) are correct

Answer

Only (i) is correct

Answer

Only (ii) is correct

Answer

Both (i) and (iv) are correct

Question 50

Adiabatic bulk modulus of a substance is defined as

Accepted Answer

−𝑣(𝜕𝑃 𝜕𝑣) 𝑠

Answer

−1 𝑣(𝜕𝑣 𝜕𝑃) 𝑇

Answer

−𝑣(𝜕𝑃 𝜕𝑣) 𝑇

Answer

−1 𝑣(𝜕𝑣 𝜕𝑃) 𝑠

Question 51

An insulated rigid closed tank of 2 m3 internal volume contains saturated liquid- vapor mixture of water at 200 ℃. The quality of the mixture is 0.75. The mass of the mixture in the tank is ____________ kg (rounded off to one decimal place). Use the following data for water: At 200 ℃: vf = 0.001156 m3/kg, vfg = 0.12620 m3/kg, vg = 0.12736 m3/kg

Accepted Answer

20.5 to 21.5

Question 52

A rigid closed tank contains 2 kg of an ideal gas at 500 kPa and 350 K. A valve is opened, and half of the mass of the gas is allowed to escape. Then the valve is closed. If the final pressure in the tank is 300 kPa, the final temperature in the tank is ____________ K (in integer).

Accepted Answer

420

Question 53

Air at 400 K and 200 kPa is heated at constant pressure to 600 K. Assuming that the internal energy is a function of temperature only, the magnitude of change in internal energy during this process is ____________ kJ/kmol (rounded off to one decimal place). Use the following data: Molar specific heat of air at constant volume: 𝑐̅𝑣 (kJ/kmol-K) = 𝑎+ 𝑏𝑇+ 𝑐𝑇2 where 𝑇 is temperature in K, 𝑎 = 19.686 kJ/kmol-K, 𝑏 = 0.002 kJ/kmol-K2 and 𝑐= 0.5 × 10−5 kJ/kmol-K3.

Accepted Answer

4389 to 4392

Question 54

A rigid closed tank having a volume of 2 m3 contains 0.1 m3 of saturated liquid water and 1.9 m3 of saturated water vapor at 100 kPa. Heat is transferred to the tank until the final tank pressure reaches 2 MPa. Following data for water is given: At 100 kPa: vf = 0.001043 m3/kg, vg = 1.694 m3/kg, uf = 417.33 kJ/kg, ug = 2506.06 kJ/kg At 2 MPa: vf = 0.001177 m3/kg, vg = 0.09963 m3/kg, uf = 906.42 kJ/kg, ug = 2600.26 kJ/kg The magnitude of heat transfer in this process is

Accepted Answer

77470 kJ

Answer

34670 kJ

Answer

55842 kJ

Answer

67906 kJ

Question 55

An ideal Diesel cycle has a compression ratio of 20 and cut-off ratio of 1.5. At the beginning of the compression stroke, air is at 100 kPa, 300 K. Use the cold-air-standard assumptions with property value cp = 1.005 kJ/kg-K. Assume cp / cv = 1.4. For this cycle, the net work output per unit mass is

Accepted Answer

335 kJ/kg

Answer

395 kJ/kg

Answer

500 kJ/kg

Answer

165 kJ/kg

Question 56

A 5 kg metal block (cp = 0.5 kJ/kg-K) at 373 K is submerged into 10 kg of water (cp = 4.2 kJ/kg-K) at 293 K in an insulated rigid container without spilling. Assuming thermal equilibrium is reached, the approximate entropy change of the universe is

Accepted Answer

0.073 kJ/K

Answer

−0.565 kJ/K

Answer

0.642 kJ/K

Answer

0.963 kJ/K

Question 57

Match the following: Thermodynamic function/equation Expression A1 Helmholtz function (a) B1 ( d d𝑇(ln 𝑃)) 𝑠𝑎𝑡 = ℎ𝑔−ℎ𝑓 𝑅𝑇2 A2 Gibbs function (g) B2 𝑢−𝑇𝑠 A3 T-ds equation B3 d𝑢= 𝑇d𝑠−𝑃d𝑣 A4 Clapeyron-Clausius equation B4 ℎ−𝑇𝑠 .

Accepted Answer

A1→B2, A2→B4, A3→B3, A4→B1

Answer

A1→B2, A2→B4, A3→B1, A4→B3

Answer

A1→B4, A2→B2, A3→B1, A4→B3

Answer

A1→B4, A2→B2, A3→B3, A4→B1

Question 58

A piston-cylinder device initially contains 1 m3 of air at 200 kPa and 25 ℃. Air expands at constant pressure while a heater of 250 W is switched on for 10 minutes. There is a heat loss of 4 kJ during this process. Assuming air as an ideal gas, the final temperature of air is ____________ ℃ (rounded off to one decimal place). Use the following data for air: R = 0.287 kJ/kg-K, cp = 1.005 kJ/kg-K

Accepted Answer

85.0 to 88.0

Question 59

Steam at 2 MPa and 300 ℃ steadily enters a nozzle of inlet diameter of 20 cm. Steam leaves the nozzle with a velocity of 300 m/s. The mass flow rate of steam through the nozzle is 10 kg/s. Assume no work interaction and no change in potential energy. If the heat loss from the nozzle per kg of steam is 3 kJ, the exit enthalpy per kg of steam is ____________ kJ (rounded off to nearest integer). Use the following data for steam: At 2 MPa and 300 ℃: v = 0.12551 m3/kg, h = 3024.2 kJ/kg

Accepted Answer

2975 to 2980

Question 60

A rigid tank of 2 m3 internal volume contains 5 kg of water as a saturated liquid-vapor mixture at 400 kPa. Half of the mass of the saturated liquid in the tank is drained-off while maintaining constant pressure of 400 kPa in the tank. The final quality of the mixture remaining in the tank is ____________ (rounded off to two decimal places). Use the following data for water: At 400 kPa: vf = 0.001084 m3/kg, vfg = 0.46138 m3/kg, vg = 0.46246 m3/kg

Accepted Answer

0.90 to 0.95

Question 61

Consider a spark ignition engine which operates on an ideal air-standard Otto cycle. It uses a fuel which produces 44 MJ/kg of heat in the engine. If the engine requires 40 mg of fuel to produce 1 kJ of work output, then the compression ratio of the Otto cycle is ____________ (rounded off to two decimal places). For the entire cycle, use cp / cv = 1.4

Accepted Answer

8.00 to 8.30

Question 62

A refrigerator operates on an ideal vapor compression cycle between the pressure limits of 140 kPa and 800 kPa. The working fluid is the refrigerant R-134a. The refrigerant enters the compressor as saturated vapor at 140 kPa and exits at 800 kPa and 60 ℃. It leaves the condenser as a saturated liquid at 800 kPa. The coefficient of performance (COP) of the refrigerator is ____________ (rounded off to two decimal places). Use the following property data for R-134a: At 140 kPa: hf = 27.06 kJ/kg, hg = 239.19 kJ/kg At 800 kPa: hf = 95.48 kJ/kg, hg = 267.34 kJ/kg At 800 kPa and 60 ℃: h = 296.82 kJ/kg

Accepted Answer

2.45 to 2.55

Question 63

A steam power plant operates on a simple ideal Rankine cycle. The condenser pressure is 10 kPa and the boiler pressure is 5 MPa. The steam enters the turbine at 600 ℃. Mass flow rate of the steam is 50 kg/s. Neglecting the pump work, the net power output of the plant is ____________ MW (rounded off to one decimal place). Use the following property data for water: At 10 kPa: hf = 191.81 kJ/kg, hfg = 2392.82 kJ/kg, hg = 2584.63 kJ/kg sf = 0.6492 kJ/kg-K, sfg = 7.5010 kJ/kg-K, sg = 8.1502 kJ/kg-K At 5 MPa and 600 ℃: h = 3666.47 kJ/kg, s = 7.2588 kJ/kg-K

Accepted Answer

67.3 to 69.3

Question 64

In an air-conditioning system, air enters at 20 ℃ and 30% relative humidity at a steady rate of 30 m3/min in a humidifier and it is conditioned to 25 ℃ and 60% relative humidity. Assuming entire process takes place at pressure of 100 kPa, the mass flow rate of the steam added to air in the humidifier is ____________ kg/min (rounded off to three decimal places). Use the following property data: At 20 ℃ and 25 ℃, saturation pressures of water are 2.3392 kPa and 3.1698 kPa, respectively. For air, R = 0.287 kJ/kg-K

Accepted Answer

0.262 to 0.290

Thermodynamics (XE-E) - GATE XE (Engineering Sciences) Subject-Wise PYQ Practice

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