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This mock test of Basic Thermodynamics for GATE helps you for every GATE entrance exam.
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QUESTION: 1

Air undergoes a polytropic process in an adiabatic nozzle with n = 1.2. Inlet state of air is 800 kPa, 123^{0}C with a velocity of 32 m/s and exit state is 300 kPa. Find out the velocity of air at nozzle exit.

Solution:

QUESTION: 2

A 5m X 8m X 0.3m size concrete slab ( ρ = 2200 kg/m^{3}, C_{P} = 0.88 kJ/kg-K) is used as thermal storage mass in solar heated house. If slab cools overnight from 23^{0}C to 18^{0}C in 18^{0}C house, what will be the net entropy change associated with process?

Solution:

**Correct Answer :- d**

**Explanation : ΔS = mCpln(T2/T1) + Q/T0**

**m = (5 * 8 * 0.3) * 2200**

**m = 26400 kg**

**T1 = 291K, T2 = 296K**

**T0 = 291K**

**ΔS = 26400 (.88ln (291/296)+.88 (296-291)/291)**

**ΔS = 3.4 KJ/K**

QUESTION: 3

Water at 95^{0}C having mass of 45 kg is filled in a container and is placed in well-insulated room. Heat transfer takes place between water and air in room till thermal equilibrium is established. Entropy generation will be: - V_{air} = 90m^{3}, T_{air} = 12^{0}C, P = 101.3kPa, CW = 4.18 kJ/kg-K, C_{P} = 1.005 kJ/K

Solution:

Answer is (d)

QUESTION: 4

The reading of the pressure gauge fitted on a vessel is 25 bar. The atmospheric pressure is 1.03 bar and the value of '*g*' is 9.81 m/s^{2}. The absolute pressure in the vessel is

Solution:

QUESTION: 5

Consider air in a cylinder volume of 0.2 L at 7 MPa, 1800K. It now expands in a reversible polytropic process with exponent, n = 1.5, through a volume ratio of 8:1. Calculate the work for the process.

Solution:

Answer is (b)

QUESTION: 6

**Common data for 6, 7 & 8:**

In adiabatic turbine, air enters at 550 kPa, 425K and leaves at 110kPa, 325K. The inlet and exit velocities of air are 150m/s and 50m/s respectively

T_{0} = 25^{0}C, C_{P} = 1.005 kJ/kg-K, R = 0.287 kJ/kg-K

**Q. **Actual work will be:-

Solution:

Answer is (d)

QUESTION: 7

**Common data for 6, 7 & 8:**

In adiabatic turbine, air enters at 550 kPa, 425K and leaves at 110kPa, 325K. The inlet and exit velocities of air are 150m/s and 50m/s respectively

T_{0} = 25^{0}C, C_{P} = 1.005 kJ/kg-K, R = 0.287 kJ/kg-K

**Q. **Reversible work will be:-

Solution:

Answer is (b)

QUESTION: 8

**Common data for 6, 7 & 8:**

In adiabatic turbine, air enters at 550 kPa, 425K and leaves at 110kPa, 325K. The inlet and exit velocities of air are 150m/s and 50m/s respectively

T_{0} = 25^{0}C, C_{P} = 1.005 kJ/kg-K, R = 0.287 kJ/kg-K

**Q. **Isentropic efficiency is: -

Solution:

Answer is (d)

QUESTION: 9

What is the effect on internal energy during adiabatic expansion process in a closed system?

Solution:

Answer is (b)

QUESTION: 10

An insulated tank contains 120L of water at 25^{0}C ( ρ = 997 kg/m^{3}, C_{P} = 4.18 kJ/kg^{0}C). A 50kg copper block (C_{P} = 0.386 kJ/kg^{0}C) initially at 80^{0}C is dropped into water. Total entropy change for this process will be:-

Solution:

QUESTION: 11

Two blocks of iron and copper, both initially at 80^{0}C, are dropped into a large lake at 15^{0}C. The mass of the iron and copper blocks are 50kg and 20 kg respectively. After a while, the system is in thermal equilibrium due to heat transfer between blocks and lake water.

Total entropy change for this process is:-

C_{iron} = 0.45 kJ/kg^{0}C, C_{copper} = 0.386 kJ/kg^{0}C

Solution:

Answer is (c)

QUESTION: 12

**A football was inflated to a gauge pressure of 1 bar when the ambient temperature was 15°C. When the game started next day, the air temperature at the stadium was 5°C. Assume that the volume of the football remains constant at 2500 cm ^{3}. Gauge pressure of air to which the ball must have been originally inflated so that it would equal 1 bar gauge at the stadium is _____.**

Solution:

QUESTION: 13

A rigid insulated tank has two equal parts by partition. First part initially contains 5k mol of an ideal gas at

500 kPa, 40^{0}C and other part is evacuated. If partition is removed, then the gas fills the entire tank, what will be the total entropy change during this process.

Solution:

Answer is (a)

QUESTION: 14

In an isobaric process, 1kg of air at 400K is mixed with 1kg of air at 500K. If pressure is 100 kPa and Q = 0, the entropy generation in process will be:-

Solution:

Answer is (a)

QUESTION: 15

Which of the following statements are true for a polytropic process.

[n < γ]

Solution:

*Answer can only contain numeric values

QUESTION: 16

A refrigeration plant for food storage operates as a reversed carnot heat engine cycle. The store is to be maintained at -5^{0}C and the heat transfer from the store to the cycle is at the rate of 5 kW. If heat is transferred from the cycle to the atmosphere at a temperature of 25^{0}C, the power required to drive the plant is ____kW

(**Important -** Enter only the numerical value in the answer)

Solution:

Answer is (0.5 - 0.6 kW)

QUESTION: 17

A 50-Kg block of iron casting at 500K is thrown into a large lake that is at a temperature of 285K. The iron block eventually reaches thermal equilibrium with the lake water. Assuming an average specific heat of 0.45 kJ/Kg-K for the iron, the entropy generation during the process is:

Solution:

Answer is (c)

QUESTION: 18

A cylinder contains 0.12m^{3} of air at 1 bar and 90^{0}C. It is compressed to 0.03m^{3}, the final pressure being 6 bar. The index of the compression will be

Solution:

Answer is (a)

*Answer can only contain numeric values

QUESTION: 19

Air at 100 KPa and 280 K is compressed steadily to 600 KPa and 400 K. The mass flow rate of air is 0.02 Kg/s and a heat loss of 16 kJ/Kg occurs during the process. The power input to compressor will be_____kW

Solution:

QUESTION: 20

**Common data for 20 & 21:**

An insulated nozzle is there in which helium gas enters with velocity of 10 m/s, operating at steady state at 1300K, 4 bar. At the exit, temperature & pressure of the helium are 900K and 1.45bar, respectively. The environment is at T_{0} = 20^{0}C and P_{0} = 1 atm.

Take C_{P} = 5.1926 kJ/kg-K, R = 2.0769 kJ/kg-K, γ = 1.667

**Q. **Exit velocity of nozzle is: -

Solution:

QUESTION: 21

**Common data for 20 & 21:**

An insulated nozzle is there in which helium gas enters with velocity of 10 m/s, operating at steady state at 1300K, 4 bar. At the exit, temperature & pressure of the helium are 900K and 1.45bar, respectively. The environment is at T_{0} = 20^{0}C and P_{0} = 1 atm.

Take C_{P} = 5.1926 kJ/kg-K, R = 2.0769 kJ/kg-K, γ = 1.667

**Q. **Rate of exergy destruction (in kJ/kg) is:-

Solution:

Answer is (b)

QUESTION: 22

Specific entropy generation when air at 1MPa, 300K is throttled to 0.5 MPa is: -

Solution:

Answer is (c)

QUESTION: 23

A refrigerator transfers 1kJ of heat from a cold region at -20^{0}C to hot region at 30^{0}C. If COP of refrigerator is 4, total entropy change of region’s will be:-

Solution:

Answer is (a)

QUESTION: 24

Air enters heat exchanger at 95 kPa and 20^{0}C with rate of 1.6 m^{3}/s. The combustion gases (C_{P} = 1.1 kJ/kg-^{0}C) enters at 180^{0}C with rate of 2.2 kg/s and leave at 95^{0}C. Rate of entropy generation is

Solution:

Answer is (d)

QUESTION: 25

Exit velocity of nozzle is 400m/s. If efficiency of nozzle is 0.88, what will be ideal exit velocity?

Solution:

Answer is (c)

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