Engineering Sciences - XE 2018 GATE Paper with solution - Set -6 Notes | Study GATE Past Year Papers for Practice (All Branches) - GATE

GATE: Engineering Sciences - XE 2018 GATE Paper with solution - Set -6 Notes | Study GATE Past Year Papers for Practice (All Branches) - GATE

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GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 1/4
XE (E): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, Cp : molar heat
capacity at constant pressure, Cv : molar heat capacity at constant volume, R : universal gas constant

Q.1  When a fixed mass of  air-water vapour mixture is heated at constant pressure,
(A) both relative and specific humidity decrease.
(B) relative humidity decreases, but specific humidity remains unchanged.
(C) specific humidity decreases, but relative humidity remains unchanged.
(D) both relative and specific humidity increase.

Q.2  For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the
magnitude of work done is
(A)
1
2
ln
P
RT
P
??
??
??
(B)
2 2 1 1
PV PV ?
(C)
1
2
ln
V
R
V
??
??
??
(D) 0

Q.3  The statement which is NOT a consequence of the first law of thermodynamics is
(A) Heat is a path function
(B) Energy is a property of a system
(C) Energy of an isolated system is not conserved
(D) A perpetual motion machine of the first kind is not possible

Q.4  For a refrigerator absorbing heat QL from a cold region and rejecting heat QH to a hot region,
the coefficient of performance is written as
(A)
L
HL
Q
QQ ?
(B)
H
HL
Q
QQ ?

(C)
HL
L
QQ
Q
?
(D)
L
H
Q
Q

Q.5  The value of the compressibility factor at the critical point evaluated using the van der Waals
equation of state is
(A)
2
7
(B)
5
8
(C)
3
8
(D)
1
7

Page 2

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 1/4
XE (E): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, Cp : molar heat
capacity at constant pressure, Cv : molar heat capacity at constant volume, R : universal gas constant

Q.1  When a fixed mass of  air-water vapour mixture is heated at constant pressure,
(A) both relative and specific humidity decrease.
(B) relative humidity decreases, but specific humidity remains unchanged.
(C) specific humidity decreases, but relative humidity remains unchanged.
(D) both relative and specific humidity increase.

Q.2  For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the
magnitude of work done is
(A)
1
2
ln
P
RT
P
??
??
??
(B)
2 2 1 1
PV PV ?
(C)
1
2
ln
V
R
V
??
??
??
(D) 0

Q.3  The statement which is NOT a consequence of the first law of thermodynamics is
(A) Heat is a path function
(B) Energy is a property of a system
(C) Energy of an isolated system is not conserved
(D) A perpetual motion machine of the first kind is not possible

Q.4  For a refrigerator absorbing heat QL from a cold region and rejecting heat QH to a hot region,
the coefficient of performance is written as
(A)
L
HL
Q
QQ ?
(B)
H
HL
Q
QQ ?

(C)
HL
L
QQ
Q
?
(D)
L
H
Q
Q

Q.5  The value of the compressibility factor at the critical point evaluated using the van der Waals
equation of state is
(A)
2
7
(B)
5
8
(C)
3
8
(D)
1
7

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 2/4

Q.6  The vapour pressure of a liquid at 8 °C is 2.7 kPa. Its enthalpy of vaporization is constant
and equal to 42700 kJ/kmol. Take R = 8.314 kJ/kmol.K. The temperature (in °C) at a vapour
pressure of 13.5 kPa is
(A)  58.7 (B) 51.4 (C) 44.3 (D)  35.2

Q.7  One kmol of an ideal gas (Cp = 21 kJ/kmol.K) undergoes a constant pressure process from
300 K to 500 K. The molar entropy of the gas at 300 K is 150 kJ/kmol.K. The molar entropy
(in kJ/kmol.K) at 500 K (up to 1 decimal place) is ________.

Q.8  A spring, having a spring constant of 350 kN/m, is initially compressed by 0.4 cm. The work
required (in J) to compress it by another 0.6 cm (up to 1 decimal place) is ________.

Q.9  An ideal gas has a molar mass of 40 kg/kmol. Take R = 8.314 kJ/kmol.K. At a pressure of
2 bar and a temperature of 300 K, the volume (in m
3
) of 1 kg of this gas (up to 2 decimal
places) is ________.

Q.10  Consider the following statements for an ideal gas undergoing a reversible non-flow process:

P. If the process is adiabatic, the change in enthalpy of the gas is necessarily zero.
Q. If the process is adiabatic, the change in entropy of the gas is necessarily zero.
R. If the process is isothermal, the change in enthalpy of the gas is necessarily zero.
S. If the process is isothermal, the change in entropy of the gas is necessarily zero.

Which one of the following options is valid?
(A) Only P is correct (B) Only S is correct
(C) Only Q and R are correct (D) Only P and S are correct

Q.11  An ideal Otto cycle (O) and an ideal diesel cycle (D) have the same maximum temperature
and reject equal amount of heat. Also, the working fluid enters at the same state before
compression. One of the following statements always true about their efficiencies (?? ) is
(A) ?? O
> ?? D
(B) ?? O
= ?? D

(C) ?? O
< ?? D
(D) ?? O
= 1 - ?? D

Q.12  A reversible engine receives 75 kJ/s of energy from a reservoir at 750 K and does 12 kJ/s of
work. The heat is rejected to two reservoirs at 650 K and 550 K. The rate of heat rejection
(in kJ/s) to the reservoir at 650 K is
(A)  11 (B) 31 (C) 41 (D)  52

Page 3

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 1/4
XE (E): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, Cp : molar heat
capacity at constant pressure, Cv : molar heat capacity at constant volume, R : universal gas constant

Q.1  When a fixed mass of  air-water vapour mixture is heated at constant pressure,
(A) both relative and specific humidity decrease.
(B) relative humidity decreases, but specific humidity remains unchanged.
(C) specific humidity decreases, but relative humidity remains unchanged.
(D) both relative and specific humidity increase.

Q.2  For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the
magnitude of work done is
(A)
1
2
ln
P
RT
P
??
??
??
(B)
2 2 1 1
PV PV ?
(C)
1
2
ln
V
R
V
??
??
??
(D) 0

Q.3  The statement which is NOT a consequence of the first law of thermodynamics is
(A) Heat is a path function
(B) Energy is a property of a system
(C) Energy of an isolated system is not conserved
(D) A perpetual motion machine of the first kind is not possible

Q.4  For a refrigerator absorbing heat QL from a cold region and rejecting heat QH to a hot region,
the coefficient of performance is written as
(A)
L
HL
Q
QQ ?
(B)
H
HL
Q
QQ ?

(C)
HL
L
QQ
Q
?
(D)
L
H
Q
Q

Q.5  The value of the compressibility factor at the critical point evaluated using the van der Waals
equation of state is
(A)
2
7
(B)
5
8
(C)
3
8
(D)
1
7

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 2/4

Q.6  The vapour pressure of a liquid at 8 °C is 2.7 kPa. Its enthalpy of vaporization is constant
and equal to 42700 kJ/kmol. Take R = 8.314 kJ/kmol.K. The temperature (in °C) at a vapour
pressure of 13.5 kPa is
(A)  58.7 (B) 51.4 (C) 44.3 (D)  35.2

Q.7  One kmol of an ideal gas (Cp = 21 kJ/kmol.K) undergoes a constant pressure process from
300 K to 500 K. The molar entropy of the gas at 300 K is 150 kJ/kmol.K. The molar entropy
(in kJ/kmol.K) at 500 K (up to 1 decimal place) is ________.

Q.8  A spring, having a spring constant of 350 kN/m, is initially compressed by 0.4 cm. The work
required (in J) to compress it by another 0.6 cm (up to 1 decimal place) is ________.

Q.9  An ideal gas has a molar mass of 40 kg/kmol. Take R = 8.314 kJ/kmol.K. At a pressure of
2 bar and a temperature of 300 K, the volume (in m
3
) of 1 kg of this gas (up to 2 decimal
places) is ________.

Q.10  Consider the following statements for an ideal gas undergoing a reversible non-flow process:

P. If the process is adiabatic, the change in enthalpy of the gas is necessarily zero.
Q. If the process is adiabatic, the change in entropy of the gas is necessarily zero.
R. If the process is isothermal, the change in enthalpy of the gas is necessarily zero.
S. If the process is isothermal, the change in entropy of the gas is necessarily zero.

Which one of the following options is valid?
(A) Only P is correct (B) Only S is correct
(C) Only Q and R are correct (D) Only P and S are correct

Q.11  An ideal Otto cycle (O) and an ideal diesel cycle (D) have the same maximum temperature
and reject equal amount of heat. Also, the working fluid enters at the same state before
compression. One of the following statements always true about their efficiencies (?? ) is
(A) ?? O
> ?? D
(B) ?? O
= ?? D

(C) ?? O
< ?? D
(D) ?? O
= 1 - ?? D

Q.12  A reversible engine receives 75 kJ/s of energy from a reservoir at 750 K and does 12 kJ/s of
work. The heat is rejected to two reservoirs at 650 K and 550 K. The rate of heat rejection
(in kJ/s) to the reservoir at 650 K is
(A)  11 (B) 31 (C) 41 (D)  52

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 3/4

Q.13  A gas obeys the following equation of state:

2
( ) ,
aP
P v b RT
T
? ? ?
where v is molar volume, and  a, b are constants with values
5
10 a
?
? J.K/Pa
2
.kmol and
2
8 10 b
?
?? m
3
/kmol. Take Cp = 30 kJ/kmol.K. At 10 bar and 500 K, the value of the
Joule-Thomson coefficient (in K/Pa) is
(A)
6
2 10
?
??  (B)
6
4 10
?
?? (C)
6
2 10
?
?  (D)
6
4 10
?
?

Q.14  In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (h = 3375.1 kJ/kg,
?? = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa,
h
?? = 191.81 kJ/kg, ?? ?? = 0.6492 kJ/kg.K, h
?? = 2583.9 kJ/kg and ?? ?? = 8.1488 kJ/kg.K. The
heat rejected in the condenser (in kJ/kg) is
(A)  1898 (B) 3796 (C) 949 (D)  2847

Q.15  Methane has compressibility factor value of 0.9 at reduced pressure of 1.0 and reduced
temperature of 1.5. For propane, the critical temperature and pressure are 369.8 K and
42.48 bar, respectively. Take R = 8.314 kJ/kmol.K. Applying the principle of corresponding
states, the molar volume of propane (in m
3
/kmol) at the same reduced pressure and
temperature is
(A)  0.355 (B) 0.526 (C) 0.791  (D)  0.977

Q.16  A rigid insulated vessel is divided into two compartments by a partition. One compartment
contains 12 kg of oxygen at 200 kPa and 280 K. The other compartment contains 26 kg of
carbon dioxide at 400 kPa and 360 K. The specific heats at constant volume in kJ/kg.K for
oxygen and carbon dioxide are 0.662 and 0.653, respectively. The partition is removed and
the gases are allowed to mix. Considering both gases are ideal, the final temperature (in K)
of the mixture (up to 1 decimal place) is ________.

Q.17  Moist air having 60% relative humidity, enters a steady-flow air-conditioning unit at 102 kPa
and 30 °C. The volume flow rate of the moist air entering the unit is 0.1 m
3
/s. The moist air
leaves the unit at 95 kPa and 15 °C with a relative humidity of 100%. Liquid condensate
leaves the unit at 15 °C.
For water: at 15 °C, h
?? = 62.982 kJ/kg, h
?? = 2528.3 kJ/kg, ?? ??????
= 1.7057 kPa.
at 30 °C, h
?? = 125.74 kJ/kg, h
?? = 2555.6 kJ/kg, ?? ??????
= 4.2469 kPa.
For air, specific heat at constant pressure is 1.004 kJ/kg.K and the specific gas constant is
0.287 kJ/kg.K.
Neglecting heat leakage to the surrounding, the magnitude of heat extracted (in kW) from
the air stream (up to 2 decimal places) is __________.

Page 4

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 1/4
XE (E): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, Cp : molar heat
capacity at constant pressure, Cv : molar heat capacity at constant volume, R : universal gas constant

Q.1  When a fixed mass of  air-water vapour mixture is heated at constant pressure,
(A) both relative and specific humidity decrease.
(B) relative humidity decreases, but specific humidity remains unchanged.
(C) specific humidity decreases, but relative humidity remains unchanged.
(D) both relative and specific humidity increase.

Q.2  For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the
magnitude of work done is
(A)
1
2
ln
P
RT
P
??
??
??
(B)
2 2 1 1
PV PV ?
(C)
1
2
ln
V
R
V
??
??
??
(D) 0

Q.3  The statement which is NOT a consequence of the first law of thermodynamics is
(A) Heat is a path function
(B) Energy is a property of a system
(C) Energy of an isolated system is not conserved
(D) A perpetual motion machine of the first kind is not possible

Q.4  For a refrigerator absorbing heat QL from a cold region and rejecting heat QH to a hot region,
the coefficient of performance is written as
(A)
L
HL
Q
QQ ?
(B)
H
HL
Q
QQ ?

(C)
HL
L
QQ
Q
?
(D)
L
H
Q
Q

Q.5  The value of the compressibility factor at the critical point evaluated using the van der Waals
equation of state is
(A)
2
7
(B)
5
8
(C)
3
8
(D)
1
7

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 2/4

Q.6  The vapour pressure of a liquid at 8 °C is 2.7 kPa. Its enthalpy of vaporization is constant
and equal to 42700 kJ/kmol. Take R = 8.314 kJ/kmol.K. The temperature (in °C) at a vapour
pressure of 13.5 kPa is
(A)  58.7 (B) 51.4 (C) 44.3 (D)  35.2

Q.7  One kmol of an ideal gas (Cp = 21 kJ/kmol.K) undergoes a constant pressure process from
300 K to 500 K. The molar entropy of the gas at 300 K is 150 kJ/kmol.K. The molar entropy
(in kJ/kmol.K) at 500 K (up to 1 decimal place) is ________.

Q.8  A spring, having a spring constant of 350 kN/m, is initially compressed by 0.4 cm. The work
required (in J) to compress it by another 0.6 cm (up to 1 decimal place) is ________.

Q.9  An ideal gas has a molar mass of 40 kg/kmol. Take R = 8.314 kJ/kmol.K. At a pressure of
2 bar and a temperature of 300 K, the volume (in m
3
) of 1 kg of this gas (up to 2 decimal
places) is ________.

Q.10  Consider the following statements for an ideal gas undergoing a reversible non-flow process:

P. If the process is adiabatic, the change in enthalpy of the gas is necessarily zero.
Q. If the process is adiabatic, the change in entropy of the gas is necessarily zero.
R. If the process is isothermal, the change in enthalpy of the gas is necessarily zero.
S. If the process is isothermal, the change in entropy of the gas is necessarily zero.

Which one of the following options is valid?
(A) Only P is correct (B) Only S is correct
(C) Only Q and R are correct (D) Only P and S are correct

Q.11  An ideal Otto cycle (O) and an ideal diesel cycle (D) have the same maximum temperature
and reject equal amount of heat. Also, the working fluid enters at the same state before
compression. One of the following statements always true about their efficiencies (?? ) is
(A) ?? O
> ?? D
(B) ?? O
= ?? D

(C) ?? O
< ?? D
(D) ?? O
= 1 - ?? D

Q.12  A reversible engine receives 75 kJ/s of energy from a reservoir at 750 K and does 12 kJ/s of
work. The heat is rejected to two reservoirs at 650 K and 550 K. The rate of heat rejection
(in kJ/s) to the reservoir at 650 K is
(A)  11 (B) 31 (C) 41 (D)  52

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 3/4

Q.13  A gas obeys the following equation of state:

2
( ) ,
aP
P v b RT
T
? ? ?
where v is molar volume, and  a, b are constants with values
5
10 a
?
? J.K/Pa
2
.kmol and
2
8 10 b
?
?? m
3
/kmol. Take Cp = 30 kJ/kmol.K. At 10 bar and 500 K, the value of the
Joule-Thomson coefficient (in K/Pa) is
(A)
6
2 10
?
??  (B)
6
4 10
?
?? (C)
6
2 10
?
?  (D)
6
4 10
?
?

Q.14  In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (h = 3375.1 kJ/kg,
?? = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa,
h
?? = 191.81 kJ/kg, ?? ?? = 0.6492 kJ/kg.K, h
?? = 2583.9 kJ/kg and ?? ?? = 8.1488 kJ/kg.K. The
heat rejected in the condenser (in kJ/kg) is
(A)  1898 (B) 3796 (C) 949 (D)  2847

Q.15  Methane has compressibility factor value of 0.9 at reduced pressure of 1.0 and reduced
temperature of 1.5. For propane, the critical temperature and pressure are 369.8 K and
42.48 bar, respectively. Take R = 8.314 kJ/kmol.K. Applying the principle of corresponding
states, the molar volume of propane (in m
3
/kmol) at the same reduced pressure and
temperature is
(A)  0.355 (B) 0.526 (C) 0.791  (D)  0.977

Q.16  A rigid insulated vessel is divided into two compartments by a partition. One compartment
contains 12 kg of oxygen at 200 kPa and 280 K. The other compartment contains 26 kg of
carbon dioxide at 400 kPa and 360 K. The specific heats at constant volume in kJ/kg.K for
oxygen and carbon dioxide are 0.662 and 0.653, respectively. The partition is removed and
the gases are allowed to mix. Considering both gases are ideal, the final temperature (in K)
of the mixture (up to 1 decimal place) is ________.

Q.17  Moist air having 60% relative humidity, enters a steady-flow air-conditioning unit at 102 kPa
and 30 °C. The volume flow rate of the moist air entering the unit is 0.1 m
3
/s. The moist air
leaves the unit at 95 kPa and 15 °C with a relative humidity of 100%. Liquid condensate
leaves the unit at 15 °C.
For water: at 15 °C, h
?? = 62.982 kJ/kg, h
?? = 2528.3 kJ/kg, ?? ??????
= 1.7057 kPa.
at 30 °C, h
?? = 125.74 kJ/kg, h
?? = 2555.6 kJ/kg, ?? ??????
= 4.2469 kPa.
For air, specific heat at constant pressure is 1.004 kJ/kg.K and the specific gas constant is
0.287 kJ/kg.K.
Neglecting heat leakage to the surrounding, the magnitude of heat extracted (in kW) from
the air stream (up to 2 decimal places) is __________.

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 4/4

Q.18  Air at 150 kPa and 323 K is filled in a rigid vessel of 0.05 m
3
capacity. For air, assumed as
an ideal gas, specific heat at constant volume is 0.7163 kJ/kg.K and the specific gas constant
is 0.287 kJ/kg.K. Neglect kinetic and potential energy changes. If 30 kJ of heat is added, the
final temperature (in K) of air (up to 1 decimal place) is __________.

Q.19  Superheated steam at 2 bar and 300 °C, with an enthalpy of 3072.1 kJ/kg, enters a horizontal
adiabatic nozzle with negligible velocity and leaves at 0.2 bar as saturated vapour with an
enthalpy of 2609.9 kJ/kg. Assuming steady flow and neglecting the potential energy changes,
the exit velocity (in m/s) of the steam (up to 1 decimal place) is __________.

Q.20  A given mass of a simple compressible substance undergoes a reversible cycle, as shown in
the P-V diagram. The magnitude of the net work done during the cycle is 3 kJ. The pressure
(in bar) at point C (up to 1 decimal place) is ________.

Q.21  One kmol of an ideal gas at 300 K and 10 bar is reversibly heated in a constant volume
process to 500 K. It is then reversibly and isothermally expanded to 2 bar. Take
Cv = 20.8 kJ/kmol.K and R = 8.314 kJ/kmol.K. The total heat supplied (in kJ) to the gas
(up to 1 decimal place) is ________.

Q.22  A rigid container is completely filled with a liquid having a constant isothermal
compressibility of
41
1.09 10 bar
??
? and a constant coefficient of volume expansion of
31
1.12 10 K
??
? . The liquid is initially at 300 K and 1 bar. Heat is supplied to the liquid to
raise its temperature to 350 K. Assuming that no phase change occurs, the final pressure
(in bar) of the liquid (up to 1 decimal place) is ________.

END OF THE QUESTION PAPER
Page 5

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 1/4
XE (E): Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Notation used:
P : pressure, V : volume, T : temperature, s : specific entropy, h : specific enthalpy, Cp : molar heat
capacity at constant pressure, Cv : molar heat capacity at constant volume, R : universal gas constant

Q.1  When a fixed mass of  air-water vapour mixture is heated at constant pressure,
(A) both relative and specific humidity decrease.
(B) relative humidity decreases, but specific humidity remains unchanged.
(C) specific humidity decreases, but relative humidity remains unchanged.
(D) both relative and specific humidity increase.

Q.2  For a reversible isothermal expansion of one mole of an ideal gas from state 1 to state 2, the
magnitude of work done is
(A)
1
2
ln
P
RT
P
??
??
??
(B)
2 2 1 1
PV PV ?
(C)
1
2
ln
V
R
V
??
??
??
(D) 0

Q.3  The statement which is NOT a consequence of the first law of thermodynamics is
(A) Heat is a path function
(B) Energy is a property of a system
(C) Energy of an isolated system is not conserved
(D) A perpetual motion machine of the first kind is not possible

Q.4  For a refrigerator absorbing heat QL from a cold region and rejecting heat QH to a hot region,
the coefficient of performance is written as
(A)
L
HL
Q
QQ ?
(B)
H
HL
Q
QQ ?

(C)
HL
L
QQ
Q
?
(D)
L
H
Q
Q

Q.5  The value of the compressibility factor at the critical point evaluated using the van der Waals
equation of state is
(A)
2
7
(B)
5
8
(C)
3
8
(D)
1
7

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 2/4

Q.6  The vapour pressure of a liquid at 8 °C is 2.7 kPa. Its enthalpy of vaporization is constant
and equal to 42700 kJ/kmol. Take R = 8.314 kJ/kmol.K. The temperature (in °C) at a vapour
pressure of 13.5 kPa is
(A)  58.7 (B) 51.4 (C) 44.3 (D)  35.2

Q.7  One kmol of an ideal gas (Cp = 21 kJ/kmol.K) undergoes a constant pressure process from
300 K to 500 K. The molar entropy of the gas at 300 K is 150 kJ/kmol.K. The molar entropy
(in kJ/kmol.K) at 500 K (up to 1 decimal place) is ________.

Q.8  A spring, having a spring constant of 350 kN/m, is initially compressed by 0.4 cm. The work
required (in J) to compress it by another 0.6 cm (up to 1 decimal place) is ________.

Q.9  An ideal gas has a molar mass of 40 kg/kmol. Take R = 8.314 kJ/kmol.K. At a pressure of
2 bar and a temperature of 300 K, the volume (in m
3
) of 1 kg of this gas (up to 2 decimal
places) is ________.

Q.10  Consider the following statements for an ideal gas undergoing a reversible non-flow process:

P. If the process is adiabatic, the change in enthalpy of the gas is necessarily zero.
Q. If the process is adiabatic, the change in entropy of the gas is necessarily zero.
R. If the process is isothermal, the change in enthalpy of the gas is necessarily zero.
S. If the process is isothermal, the change in entropy of the gas is necessarily zero.

Which one of the following options is valid?
(A) Only P is correct (B) Only S is correct
(C) Only Q and R are correct (D) Only P and S are correct

Q.11  An ideal Otto cycle (O) and an ideal diesel cycle (D) have the same maximum temperature
and reject equal amount of heat. Also, the working fluid enters at the same state before
compression. One of the following statements always true about their efficiencies (?? ) is
(A) ?? O
> ?? D
(B) ?? O
= ?? D

(C) ?? O
< ?? D
(D) ?? O
= 1 - ?? D

Q.12  A reversible engine receives 75 kJ/s of energy from a reservoir at 750 K and does 12 kJ/s of
work. The heat is rejected to two reservoirs at 650 K and 550 K. The rate of heat rejection
(in kJ/s) to the reservoir at 650 K is
(A)  11 (B) 31 (C) 41 (D)  52

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 3/4

Q.13  A gas obeys the following equation of state:

2
( ) ,
aP
P v b RT
T
? ? ?
where v is molar volume, and  a, b are constants with values
5
10 a
?
? J.K/Pa
2
.kmol and
2
8 10 b
?
?? m
3
/kmol. Take Cp = 30 kJ/kmol.K. At 10 bar and 500 K, the value of the
Joule-Thomson coefficient (in K/Pa) is
(A)
6
2 10
?
??  (B)
6
4 10
?
?? (C)
6
2 10
?
?  (D)
6
4 10
?
?

Q.14  In an ideal Rankine cycle, steam enters the turbine at 10 MPa and 500 °C (h = 3375.1 kJ/kg,
?? = 6.5995 kJ/kg.K). It is cooled in the condenser at a pressure of 10 kPa. At 10 kPa,
h
?? = 191.81 kJ/kg, ?? ?? = 0.6492 kJ/kg.K, h
?? = 2583.9 kJ/kg and ?? ?? = 8.1488 kJ/kg.K. The
heat rejected in the condenser (in kJ/kg) is
(A)  1898 (B) 3796 (C) 949 (D)  2847

Q.15  Methane has compressibility factor value of 0.9 at reduced pressure of 1.0 and reduced
temperature of 1.5. For propane, the critical temperature and pressure are 369.8 K and
42.48 bar, respectively. Take R = 8.314 kJ/kmol.K. Applying the principle of corresponding
states, the molar volume of propane (in m
3
/kmol) at the same reduced pressure and
temperature is
(A)  0.355 (B) 0.526 (C) 0.791  (D)  0.977

Q.16  A rigid insulated vessel is divided into two compartments by a partition. One compartment
contains 12 kg of oxygen at 200 kPa and 280 K. The other compartment contains 26 kg of
carbon dioxide at 400 kPa and 360 K. The specific heats at constant volume in kJ/kg.K for
oxygen and carbon dioxide are 0.662 and 0.653, respectively. The partition is removed and
the gases are allowed to mix. Considering both gases are ideal, the final temperature (in K)
of the mixture (up to 1 decimal place) is ________.

Q.17  Moist air having 60% relative humidity, enters a steady-flow air-conditioning unit at 102 kPa
and 30 °C. The volume flow rate of the moist air entering the unit is 0.1 m
3
/s. The moist air
leaves the unit at 95 kPa and 15 °C with a relative humidity of 100%. Liquid condensate
leaves the unit at 15 °C.
For water: at 15 °C, h
?? = 62.982 kJ/kg, h
?? = 2528.3 kJ/kg, ?? ??????
= 1.7057 kPa.
at 30 °C, h
?? = 125.74 kJ/kg, h
?? = 2555.6 kJ/kg, ?? ??????
= 4.2469 kPa.
For air, specific heat at constant pressure is 1.004 kJ/kg.K and the specific gas constant is
0.287 kJ/kg.K.
Neglecting heat leakage to the surrounding, the magnitude of heat extracted (in kW) from
the air stream (up to 2 decimal places) is __________.

GATE 2018                                                                                                                                                                                    Thermodynamics (XE-E)
XE-E 4/4

Q.18  Air at 150 kPa and 323 K is filled in a rigid vessel of 0.05 m
3
capacity. For air, assumed as
an ideal gas, specific heat at constant volume is 0.7163 kJ/kg.K and the specific gas constant
is 0.287 kJ/kg.K. Neglect kinetic and potential energy changes. If 30 kJ of heat is added, the
final temperature (in K) of air (up to 1 decimal place) is __________.

Q.19  Superheated steam at 2 bar and 300 °C, with an enthalpy of 3072.1 kJ/kg, enters a horizontal
adiabatic nozzle with negligible velocity and leaves at 0.2 bar as saturated vapour with an
enthalpy of 2609.9 kJ/kg. Assuming steady flow and neglecting the potential energy changes,
the exit velocity (in m/s) of the steam (up to 1 decimal place) is __________.

Q.20  A given mass of a simple compressible substance undergoes a reversible cycle, as shown in
the P-V diagram. The magnitude of the net work done during the cycle is 3 kJ. The pressure
(in bar) at point C (up to 1 decimal place) is ________.

Q.21  One kmol of an ideal gas at 300 K and 10 bar is reversibly heated in a constant volume
process to 500 K. It is then reversibly and isothermally expanded to 2 bar. Take
Cv = 20.8 kJ/kmol.K and R = 8.314 kJ/kmol.K. The total heat supplied (in kJ) to the gas
(up to 1 decimal place) is ________.

Q.22  A rigid container is completely filled with a liquid having a constant isothermal
compressibility of
41
1.09 10 bar
??
? and a constant coefficient of volume expansion of
31
1.12 10 K
??
? . The liquid is initially at 300 K and 1 bar. Heat is supplied to the liquid to
raise its temperature to 350 K. Assuming that no phase change occurs, the final pressure
(in bar) of the liquid (up to 1 decimal place) is ________.

END OF THE QUESTION PAPER
Q.No. Type Section Key/Range Marks
1 MCQ GA A 1
2 MCQ GA C 1
3 MCQ GA B 1
4 MCQ GA B 1
5 MCQ GA B 1
6 MCQ GA A 2
7 MCQ GA D 2
8 MCQ GA D 2
9 MCQ GA B 2
10 MCQ GA C 2
2 MCQ XE-AA 1
3 NAT XE-A 0.01 to 0.01 1
4 NAT XE-A5 to 51
5 NAT XE-A 0.29 to 0.32 1
6 NAT XE-A 250 to 250 1
7 NAT XE-A 108 to 108 1
8 MCQ XE-AB 2
9 MCQ XE-AC 2
10 NAT XE-A3 to 32
11 NAT XE-A 0.04 to 0.04 2
1 MCQ XE-BB 1
2 MCQ XE-BA 1
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