GATE 2019 Paper with Answer Keys for Thermodynamics (XE-E) - Grad Plus

# GATE 2019 Paper with Answer Keys for Thermodynamics (XE-E)

Q. 1 – Q. 9 carry one mark each & Q. 10 – Q. 22 carry two marks each.

Notations used:

cp: Specific heat at constant pressure; cv: Specific heat at constant volume; h: Specific enthalpy; s: Specific entropy; v: Specific volume; P: Pressure; V: Volume; T: Temperature; R: Gas constant; Ru : Universal Gas constant

Q.1- One kg of an ideal gas (molecular weight = X) occupies a certain volume V at temperature T and pressure ????1 . Four kgs of another ideal gas (molecular weight = 2X) is added to the first gas keeping the volume V and temperature T same as before. The final pressure is

(A) 2 P1

(B) 3 P1

(C) 4 P1

(D) 5 P1

Ans: (B) 3 P1

Q.2- Which of the following is an intensive thermodynamic property?

(A) Enthalpy

(B) Internal energy

(C) Entropy

(D) Pressure

Ans: (D) Pressure

Q.3- A thermodynamic process for a substance is represented as a constant pressure process on a P-V diagram, and a constant temperature process on a T-V diagram. Which of the following statements is TRUE?

(A) The substance is an ideal gas.

(B) The substance is a van der Waals gas.

(C) The substance undergoes a phase change.

(D) Such a process is not possible.

Ans: (C) The substance undergoes a phase change.

Q.4- Addition of a reheat process to a simple Rankine cycle will always

(A) increase both efficiency and work output of the cycle.

(B) increase efficiency but not necessarily work output of the cycle.

(C) increase work output but not necessarily efficiency of the cycle.

(D) decrease both efficiency and work output of the cycle.

Ans: (C) increase work output but not necessarily efficiency of the cycle.

Q.5- A Carnot cycle implemented using an ideal gas in a piston-cylinder system will have

(A) work transfer in two parts of the cycle and heat transfer in the other two parts of the cycle.

(B) work transfer in all four parts of the cycle and heat transfer in two parts of the cycle.

(C) work transfer in two parts of the cycle and heat transfer in all four parts of the cycle.

(D) work transfer in all four parts of the cycle and heat transfer in all four parts of the cycle.

Ans: (B) work transfer in all four parts of the cycle and heat transfer in two parts of the cycle.

Q.6- The “degrees of freedom” for a pure substance at its triple point is

(A) 3

(B) 2

(C) 1

(D) 0

Ans: (D) 0

Q.7- The differential of the Gibbs function (g) for a simple compressible system can be represented as ???????? = ???? ???????? − ???? ????????. Using the appropriate Maxwell relation derived from the above equation, the quantity, \left[-{\left(\frac{\partial s}{\partial P}\right)}_T\right] for an ideal gas is

(A) \frac RT

(B) \frac RT

(C) \frac PR

(D) \frac TR

Ans: (B) \frac RT

Q.8- A Carnot engine receives 2000 kJ heat from a source at 1200 K and rejects 500 kJ heat to sink. The sink temperature (K) is __.

Ans: 300 to 300

Q.9- A closed vessel contains a pure substance with 0.1 m3 of saturated liquid and 0.9 m3 of saturated vapor. The specific volume of the liquid and vapor phases are 0.000843 m3/kg and 0.02671 m3/kg respectively. The percentage of vapor in the mixture on mass basis (rounded off to two decimal places) is __.

Ans: 22.00 to 22.30

Q.10- A gas obeys the van der Waals equation of state \left(P+\frac a{v^2}\right)\left(v-b\right)=RT , where a and b are van der Waals constants. The compressibility factor \left[Z=\frac{Pv}{RT}\right] in the limit of high specific volume (???? ≪ ????) is

(A) 1+\frac1v\left(b-\frac a{RT}\right)

(B) 1+\frac1v\left(b+\frac a{RT}\right)

(C) 1-\frac1v\left(b+\frac a{RT}\right)

(D) 1-\frac1v\left(b-\frac a{RT}\right)

Ans: (A) 1+\frac1v\left(b-\frac a{RT}\right)

Q.11 Consider the thermodynamic relation, {\left(\frac{\partial cp}{\partial P}\right)}_T=-T{\left(\frac{\partial^2v}{\partial T^2}\right)}_P. For a certain gas, if the isobaric thermal expansion coefficient, \alpha=\frac1T (where T is the temperature measured in K), then the value of {\left(\frac{\partial cp}{\partial p}\right)}_T is,

(A) 0

(B) 1

(C) 2

(D) \frac vT

Ans: (A) 0

Q.12- A piston-cylinder system has an initial volume of 0.1 m3 and contains an ideal gas ( ???????? = 0.74 kJ/kg.K, ???? = 0.288 kJ/kg.K) at 1.5 bar and 298 K. The piston is moved to compress the gas until the pressure and temperature reach 10 bar and 423 K respectively. During this process, 20 kJ of work is done on the gas. The magnitude of heat transfer (kJ) during this process is

(A) 134.8

(B) 36.2

(C) 8.2

(D) 3.8

Ans: (D) 3.8

Q.13- A reversible cyclic device absorbs 400 kJ/s heat from a reservoir maintained at 265 K and rejects heat to another reservoir at 298 K. The magnitude of the rate of work done (kW) by the device is

(A) 849.81

(B) 449.81

(C) 355.70

(D) 49.81

Ans: (D) 49.81

Q.14- In a reversible process, an ideal gas (cp = 1.04 kJ/kg.K, R = 0.297 kJ/kg.K) at 293 K, is compressed in a cylinder from 100 kPa to 500 kPa. During this compression process, the relation between pressure and volume is expressed as, ????????1.3 = constant. In the following options, mark the closest value for the entropy change per kilogram (J/kg.K).

(A) -91

(B) 91

(C) -864

(D) 864

Ans: (A) -91

Q.15- The sublimation pressure of water vapor at 233 K is 13 Pa. Assume the water vapor to behave as an ideal gas (R = 0.46 kJ/kg.K), and the latent heat of sublimation is 2840 kJ/kg. The sublimation pressure of water vapor at 213 K, (rounded off to 2 decimal places), is _ Pa.

Ans: 1.05 to 1.15

Q.16- In a heating and humidification process, dry air (d.a) with relative humidity of 10% at ambient temperature of 100C, is mixed with superheated steam at temperature ‘T’. The resultant mixture is at 250C with relative humidity of 50%. The total pressure before and after the process remains the same at 102 kPa. The saturated pressure of water vapor (v) at 100C and 250C are 1.2281 kPa, and 3.1698 kPa, respectively. The specific humidity in
???? grams of water vapour per kg of dry air, can be calculated using\omega=622\frac{pv}{pd.a} , where ???????? ????.???? and ????????.???? are the partial pressures of water vapour and dry air respectively. The quantity of steam in grams (rounded off to 2 decimal places) added per kg of dry air is __.

Ans: 8.50 to 9.50

Q.17- In a vapor compression system, a refrigerant leaves the evaporator and enters the compressor in saturated vapor condition at 0oC. The specific enthalpies of the saturated liquid and the saturated vapor at 0oC are 50 kJ/kg and 250 kJ/kg, respectively. The refrigerant leaves the compressor with a specific enthalpy of 300 kJ/kg. From the exit of the condenser, the refrigerant is throttled to the evaporator pressure. If the coefficient of performance (COP) of the refrigerator is 2.8 then the dryness fraction of the refrigerant entering the evaporator is __.

Ans: 0.3 to 0.3

Q.18- Hot air, assumed as an ideal gas (cp = 1000 J/kg.K, γ = 1.4) enters a gas turbine at 10 bar, 1000 K and leaves at a pressure of 5 bar. Subsequently it expands in a nozzle to a pressure of 1 bar. Assume both these processes to be reversible and adiabatic. If the inlet velocity of
the air to the nozzle is negligible, the final velocity (m/s, rounded off to 1 decimal place) of air at the exit of the nozzle is __.

Ans: 770.0 to 785.0

Q.19-

The “T-s diagram” for a thermodynamic process is shown in the figure. The heat transferred (kJ/kg) during the reversible process 1-3 is __.

Ans: 255 to 255

Q.20- In a simple Rankine cycle, superheated steam enters the turbine at 100 bar, 500oC (h =3375.1 kJ/kg, s = 6.5995 kJ/kg.K) at a rate of 1000 kg/s. It expands isentropically in the turbine to the condenser pressure. The temperature in the condenser is 30oC (hf = 125.74kJ/kg, sf = 0.4368 kJ/kg.K, hg = 2555.6 kJ/kg, sg = 8.4520 kJ/kg.K). Saturated water from the condenser is pumped back to the boiler. Neglecting the pump work, the efficiency (in percentage, rounded off to 1 decimal) of the cycle is __.

Ans: 41.0 to 43.5

Q.21- A rigid, adiabatic container has two parts (A) and (B) separated by a piston. Initially, part (A) is filled with 1 kg of an ideal gas (cv = 750 J/kg.K, R = 500 J/kg.K) at 1 bar, 600 K. The part (B) is filled with 1 kg of the same ideal gas at 2 bar, 400 K. The piston is now removed. In the final state, the pressure (bar, rounded off to two decimal places) will be ___.

Ans: 1.25 to 1.25

Q.22- In a steady flow process, superheated steam at 70 bar and 450C, is throttled to 30 bar in an insulated valve, at a rate of 2 kg/s. The changes in the kinetic energy and potential energy during the process are assumed to be zero. The rate of entropy generation (kJ/s.K rounded off to three decimal places) during the throttling process is __.

The thermodynamic property data for superheated steam at 70 bar and 450oC:
h = 3288.3 kJ/kg, s = 6.6353 kJ/kg.K
The thermodynamic property data for superheated steam at 30 bar are given in the following table.

Ans: 0.700 to 0.750

END OF THE QUESTION PAPER

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