Unit II: Second Law and Entropy - Problems for Practice with Answer

 1. A reversible heat engine operates between a source at 800°C and a sink at 30°C. What is br the least rate of heat rejection per kW net work output of the engine?

2. A reversible heat engine working between 400°C and 100°C drives a heat pump which pumps heat from 0°C to 35°C. For an input 10 kW to the engine, determine the rate at which the heat is pumped to the receiver at 35°C.

[Ans:- Q = 39.25 kW]

3. A house which was heated by electric resistance heaters consumed 1200 kWh of electric energy in a winter month. If this house is heated by a heat pump instead which is having 20% COP compared to the ideal Carnot pump, the room temperature is 24.4°C while surroundings is at 0°C. Determine COP and money saved per month if the cost of electricity is Rs. 2/kWh.

[Ans:- COP = 2.44, Money saved/month = Rs. 983.606]

4. It is proposed to utilize 8500 kJ/h from a heat source at 500 K. The engine is designed to produce 1 kW operating continuously between source and atmosphere as sink. The atmospheric temperatures are 37°C in summer to 0°C in winter. Comment on the performance of the proposed engine.

[Ans:- The proposed engine will work satisfactorily in winter but for the summer, the engine should be redesigned.]

5. Two reversible heat engines A and B are arranged in series engine A rejects heat directly to engine B. Engine A receives 200 kJ at a temperature of 421°C from a hot source while engine B is in communication with a cold sink at a temperature of 4.4°C. If the work output of engine A is twice that of engine B, find

(a) The intermediate temperature and efficiency of each engine.

(b) The heat rejected to cold sink.

[Ans:- T2 = 416.42 K (or) = 143.42°C, ηA = 4.004%, ηB = 33.39, Q = 79.89 kJ]

6. Two vessels A and B each of volume 3 m3 may be connected by a tube of negative volume. Vessel A contains air at 0.7 MPa, 95°C while B contains air at 0.35 MPa, 205°C. Find the change of entropy when A is connected to B by working from first principles and assuming the mixing to be complete and adiabatic. For air assume Cp = 1.005 kJ/kg K and R = 0.287 kJ/kg K.

[Ans:-  ΔS = 0.197 kJ/K]

7. Two Carnot engines C1 and C2 work in series between two reservoirs at (T1)1000°C and (T2)37°C. If the heat received by C1 from T1 is 5 MJ and efficiency of C1 is 1.25 times that of C2. Estimate the output from C1 and C2.

[Ans:- C1 = 2737.33 kJ and C2 = 1044.99 kJ]

8. A reversible engine receives heat from a reservoir at 700°C and rejects heat at temperature T2. A second reversible engine receives the heat rejected by the first engine and rejects to a sink at temperature of 37°C. Calculate the temperature T2 for (i) equal efficiency for both the engine (ii) equal work output for both the engines.

[Ans:- 276.21°C, 368.5°C]

9. A refrigerator removes heat from the refrigerated space at 2°C at the rate of 300 kJ/min and rejects heat to the kitchen air at 26°C at the rate of 345 kJ/min. Verify whether this is violation to II law by (i) Carnot theorem principle (ii) Clausius in equality.