GATE 2021 Question Paper XE E Engineering Sciences - Thermodynamics

Q.1 - Q.7 Multiple Choice Question (MCQ), carry ONE mark each (for each wrong
answer: – 1/3).

Q.1 A refrigerator working on a reversed Carnot cycle has a Coefficient of
Performance (COP) of 4. If it works as a heat pump and consumes work input
of 1 kW, the heating effect will be:

(A) 1 kW

(B) 4 kW

(C) 5 kW

(D) 6 kW

Q.2 The liquid phase of a pure substance is termed as __________________, if its
temperature is lower than the saturation temperature corresponding to its
pressure 𝑷.

(A) super-heated liquid

(B) sub-cooled liquid

(C) metastable liquid

(D) flashing liquid

XE(E) - Copyright © GATE 2021 Page 1 of 12

Q.3 Two air streams of mass flow rates 𝒎̇𝟏 and 𝒎̇𝟐 enter a mixing chamber and exit
after perfect mixing. The corresponding temperatures of the inlet streams are
𝑻𝟏 and 𝑻𝟐 , respectively. Heat loss rate from the mixing chamber to the
surrounding is 𝑸̇. Assume that the process is steady, specific heat capacity is
constant, and air behaves as an ideal gas. Identify the correct expression for the
final exit temperature 𝑻𝟑 after mixing. The mass specific heat capacities of the
gas at constant volume and constant pressure are 𝒄𝒗 and 𝒄𝒑 , respectively.
Neglect the bulk kinetic and potential energies of the streams.

𝑚̇1 𝑇1 + 𝑚̇2 𝑇2 𝑄̇
(A) 𝑇3 = −
𝑚̇1 + 𝑚̇2 𝑐𝑣 (𝑚̇1 + 𝑚̇2 )

𝑚̇1 𝑇1 + 𝑚̇2 𝑇2 𝑄̇
(B) 𝑇3 = +
𝑚̇1 + 𝑚̇2 𝑐𝑝 (𝑚̇1 + 𝑚̇2 )

𝑚̇1 𝑇1 + 𝑚̇2 𝑇2 𝑄̇
(C) 𝑇3 = −
𝑚̇1 + 𝑚̇2 𝑐𝑝 (𝑚̇1 + 𝑚̇2 )

𝑚̇1 𝑇1 + 𝑚̇2 𝑇2 𝑄̇
(D) 𝑇3 = +
𝑚̇1 + 𝑚̇2 𝑐𝑣 (𝑚̇1 + 𝑚̇2 )

XE(E) - Copyright © GATE 2021 Page 2 of 12

Q.4 If
𝒉 is the mass specific enthalpy,
𝒔 is the mass specific entropy,
𝑷 is the pressure,
𝑻 is the temperature,
𝑪𝑽 is the mass specific heat at constant volume,
𝑪𝑷 is the mass specific heat at constant pressure,
𝜷 is the coefficient of thermal expansion,
𝒗 is the mass specific volume,
𝜿 is the isothermal compressibility,
𝝏𝒉
then the partial derivative ( 𝝏𝒔 ) =
𝑷

1 𝐶𝑃
(A) (𝑇 − ) ( )
𝛽 𝐶𝑉

1
(B) (𝑇 − )
𝛽

𝑣𝛽
(C) 𝑇 (1 − )
𝜅𝐶𝑉

(D) 𝑇

XE(E) - Copyright © GATE 2021 Page 3 of 12

Q.5 If
𝒗 is the mass specific volume,
𝒔 is the mass specific entropy,
𝑷 is the pressure,
𝑻 is the temperature,
𝝏𝒔
then using Maxwell relations, (𝝏𝑷) =
𝑻

𝜕𝑣
(A) ( )
𝜕𝑇 𝑃

𝜕𝑣
(B) − ( )
𝜕𝑇 𝑃

𝜕𝑣
(C) ( )
𝜕𝑇 𝑠

𝜕𝑣
(D) − ( )
𝜕𝑇 𝑠

Q.6 A closed system consists of a solution of liquid water and ethanol in
equilibrium with its vapours. Using the Gibbs phase rule, the degree of
freedom of the system is:

(A) 0

(B) 1

(C) 2

(D) 3

Q.7 For a real gas passing through an insulated throttling valve, the outlet
temperature of the gas ___________________ with respect to the inlet
temperature.

(A) is always higher

(B) is always lower

(C) may be higher, lower or same

(D) is always same

XE(E) - Copyright © GATE 2021 Page 4 of 12

Q.8 Multiple Select Question (MSQ), Carry ONE mark each (no negative marks).

Q.8 Atmospheric air with Dry Bulb Temperature (DBT) of 24°C and Relative
Humidity of 35%, entering in a circular duct (assume no pressure drop in the
duct) is heated by an electrical resistance arrangement inside the duct. The
DBT of air measured at the outlet of the duct is equal to 30°C. Considering the
flow to be steady, which of the following statement(s) is (are) correct as regards
to the outlet air, with respect to the inlet air?

(A) There is no change in the Relative Humidity

(B) There is no change in the Dew Point Temperature

(C) There is no change in the Specific Humidity

(D) There is no change in the Specific Enthalpy

XE(E) - Copyright © GATE 2021 Page 5 of 12

Q.9 Numerical Answer Type (NAT), carry ONE mark each (no negative marks).

Q.9 A cylinder of volume 1 m3 contains a mixture of CO2 (20% by mol) and O2
(80% by mol) at 100 kPa and 300 K. This cylinder is connected to a 1 MPa
pressure line carrying N2 at 300 K. The cylinder is filled isothermally till the
pressure of gas mixture inside it becomes 500 kPa, and then the filling is
stopped. The amount of N2 gas that has entered the cylinder is _________ (in
mole, 2 decimal places).
The universal gas constant is 8.3145 J/(mol K).

XE(E) - Copyright © GATE 2021 Page 6 of 12

Q. 10 – Q. 13 Multiple Choice Question (MCQ), carry TWO marks each (for each wrong
answer: – 2/3).

Q. 10 The saturation pressure 𝑷𝒔𝒂𝒕 of a pure liquid is represented by an equation of the
form:
𝐥𝐧 𝑷𝒔𝒂𝒕 = 𝐀 – (𝐁/𝑻),
where, 𝐀 and 𝐁 are constants, and T is the absolute temperature. For this
substance, which of the following expression for specific entropy difference
between the saturated vapour and the saturated liquid phase (𝒔𝒇𝒈) is correct?
Note: Subscripts f and g refer to saturated liquid and saturated vapour phases,
respectively, and 𝒗𝒇𝒈 is the specific volume difference between the saturated
vapour and the saturated liquid phases.
2
𝐵𝑃𝑠𝑎𝑡
(A) 𝑠𝑓𝑔 = 𝑣𝑓𝑔
𝑇2
𝐵𝑃𝑠𝑎𝑡
(B) 𝑠𝑓𝑔 = 𝑣𝑓𝑔
𝑇2
𝐵𝑃𝑠𝑎𝑡
(C) 𝑠𝑓𝑔 = 𝑣𝑓𝑔
𝑇3
3
𝐵𝑃𝑠𝑎𝑡
(D) 𝑠𝑓𝑔 = 𝑣𝑓𝑔
𝑇2

Q. 11 For a refrigeration cycle, the ratio of actual COP to the COP of a reversible
refrigerator operating between the same temperature limits is 0.8. The
condenser and evaporator temperatures are 51°C and −30°C, respectively. If
the cooling capacity of the plant is 2.4 kW, then the power input to the
refrigerator is:
(COP: Coefficient of Performance)

(A) 1.00 kW

(B) 1.33 kW

(C) 1.25 kW

(D) 2.08 kW

XE(E) - Copyright © GATE 2021 Page 7 of 12

Q. 12 Two identical pressure cookers, Cooker A and Cooker B, each having a total
internal capacity of 6 litres are available. Cooker A is filled with 2 litres of
liquid water at 110°C and Cooker B is filled with 4 litres of liquid water at
110°C. The remaining space in both the cookers is filled with saturated water
vapour in equilibrium with the liquid water. If 𝒈 represents the specific Gibbs
free energy, and subscripts 𝒗 and 𝒍 represent the saturated vapour and the
saturated liquid phases, respectively, which of the following expressions is
correct?

Vapour Vapour

Liquid Liquid
Cooker A Cooker B

(A) 𝑔𝑣,𝐴 > 𝑔𝑙,𝐵

(B) 𝑔𝑣,𝐴 < 𝑔𝑙,𝐵

(C) 𝑔𝑣,𝐴 = 𝑔𝑙,𝐵

(D) 𝑔𝑙,𝐵 = 2 𝑔𝑙,𝐴

XE(E) - Copyright © GATE 2021 Page 8 of 12

Q. 13 Four different Entropy (S) - Temperature (T) diagrams, representing liquid to
vapour phase transition process of a pure substance in a closed system under
constant pressure are shown. The diagram, which correctly represents the
process, is:

(A) 1

(B) 2

(C) 3

(D) 4

XE(E) - Copyright © GATE 2021 Page 9 of 12

Q. 14 – Q. 22 Numerical Answer Type (NAT), carry TWO marks each (no negative
marks).

Q. 14 Air having a mass flow rate of 2 kg/s enters a diffuser at 100 kPa and 30°C, with
a velocity of 200 m/s. Exit area of the diffuser is 400 cm2 while the exit temperature
of the air is 45°C. The rate of heat loss from the diffuser to the surrounding is 8
kJ/s. The pressure at the diffuser exit is ____________ kPa (2 decimal places).
For air, the characteristic gas constant is 287 J/(kgK) and specific heat capacity
at constant pressure is 1005 J/(kgK). Assume air to be an ideal gas and the flow
in the diffuser is steady.

Q. 15 For the Refrigerant R-134 (at 1 MPa and 50℃), the difference between the
specific volume computed by assuming it to be an ideal gas and its actual
specific volume is: 𝒗𝒊𝒅𝒆𝒂𝒍 − 𝒗𝒂𝒄𝒕𝒖𝒂𝒍 = 4.529 × 10−3 m3/kg. If the compressibility
factor associated with this state is 𝒁 = 𝟎. 𝟖𝟒, then 𝒗𝒄𝒐𝒎 − 𝒗𝒂𝒄𝒕𝒖𝒂𝒍 =
_______________ ×10−3 m3/kg (3 decimal places).
Here 𝒗𝒄𝒐𝒎 is the specific volume calculated using the compressibility factor.
For Refrigerant R-134 (at 1 MPa and 50℃):
The characteristic gas constant: 0.0815 kJ/(kgK), The critical pressure and
temperature are, respectively, 𝑷𝒄𝒓 = 4.059 MPa and 𝑻𝒄𝒓 = 374.2 K.

Q. 16 A mixture of air and water vapour enters a steady-flow adiabatic saturator at
50℃ and 100 kPa. It leaves the saturator in a completely saturated state at
temperature of 25℃ and pressure of 100 kPa. Liquid water enters the
saturator at 25℃. If air is considered to be an ideal gas, with constant specific
heat capacity, the relative humidity of the air entering the saturator is ______
% (1 decimal place).
Use the following data:
at 25℃ 𝒉𝒇 = 104.87 kJ/kg, 𝒉𝒈 = 2547.17 kJ/kg, 𝑷𝒔𝒂𝒕 =3.161 kPa
at 50℃ 𝒉𝒇 = 209.31 kJ/kg, 𝒉𝒈 = 2592.06 kJ/kg, 𝑷𝒔𝒂𝒕 =12.335 kPa
Specific heat capacity of air at constant pressure 𝑪𝑷 =1.005 kJ/(kgK)

XE(E) - Copyright © GATE 2021 Page 10 of 12

Q. 17 Air at a pressure of 1 MPa and 300 K is flowing in a pipe. An insulated
evacuated rigid tank is connected to this pipe through an insulated valve. The
volume of the tank is 1 m3. The valve is opened and the tank is filled with air
until the pressure in the tank is 1 MPa. Subsequently, the valve is closed.
Consider air to be an ideal gas and neglect bulk kinetic and potential energy.
The final temperature of air in the tank is _______ K (1 decimal place).
Specific heat capacity of air at constant pressure 𝑪𝑷 =1.005 kJ/(kgK) and
characteristic gas constant for air = 0.287 kJ/(kgK)

Q. 18 A cylinder of volume 0.1 m3 is filled with 100 mol of propane (C3H8) at 2 MPa.
If propane is assumed to obey the van der Waals equation of state, then its
temperature is ______ K (1 decimal place).
The van der Waals constants for propane are: 𝒂 = 𝟗𝟑𝟗. 𝟐 kPa (m3/kmol)2 and
𝒃 = 0.0905 m3/kmol. The universal gas constant is 8.3145 J/(mol K).

Q. 19 A frictionless piston cylinder device contains 1 kg of an ideal gas. The gas is
compressed according to 𝑷𝒗𝟏.𝟑 = constant (𝑷 is pressure and 𝒗 is mass specific
volume), from 100 kPa, 250 K, till it reaches a temperature of 500 K. The heat
transfer from the piston cylinder device to its surroundings is ______________
kJ (2 decimal places).
The characteristic gas constant is 287 J/(kgK) and the ratio of specific heat
capacities is 1.4.

Q. 20 A 0.8 m3 insulated rigid tank contains 1.5 kg of an ideal gas at 100 kPa. Electric
work is done on the system until the pressure in the tank rises to 135 kPa. The
loss in availability (exergy) associated with the process is __________ kJ (2
decimal places).
For the ideal gas, the characteristic gas constant is 188.9 J/(kgK) and the
specific heat capacity at constant volume is 680 J/(kgK). The temperature of the
dead state is 298 K.

Q.21 A rigid tank contains 1.0 kg of pure water consisting of liquid and vapour
phases in equilibrium at 10 bar. If the liquid and vapour phase each occupies
one half of the volume of the tank, then the net enthalpy of the contents of the
tank is ________ kJ (1 decimal place).
For saturated liquid and vapour at 10 bar, the thermodynamic data table
provides the following values:
𝒗𝒇 = 𝟏. 𝟏𝟐𝟕 × 𝟏𝟎−𝟑 m3/kg, 𝒗𝒈 = 𝟏𝟗𝟒. 𝟑 × 𝟏𝟎−𝟑 m3/kg,
𝒉𝒇 = 𝟕𝟔𝟐. 𝟔 kJ/kg, 𝒉𝒈 = 𝟐𝟕𝟕𝟔. 𝟐 kJ/kg

XE(E) - Copyright © GATE 2021 Page 11 of 12

Q.22 An air-standard Diesel cycle with a compression ratio of 16 takes air at 1 bar
and 300 K. If the maximum temperature in the cycle is 2100 K, then the
thermal efficiency of the cycle is _______ % (1 decimal place).
The ratio of the specific heat capacities of air is 1.4.

END OF THE QUESTION PAPER

XE(E) - Copyright © GATE 2021 Page 12 of 12