Heat Engine and Efficiency - UNSOLVED PRACTICE SET

Q7. Define the efficiency of a heat engine. Write its expression in terms of Q₁ (heat absorbed) and Q₂ (heat rejected).

Q8. Explain why the efficiency of a heat engine can never be 100%, even if there are no friction or other mechanical losses.

Q9. Draw a schematic diagram of a heat engine, labeling the source, sink, working substance, and the direction of heat and work flow.

Q10. What is a thermal reservoir? Why is it important in the analysis of heat engines?

Q11. A heat engine has an efficiency of 25%. If it rejects 600 J of heat per cycle, how much heat does it absorb? Show your calculation.

Q12. Explain the difference between a reversible heat engine and an irreversible heat engine. Give one example of each.

Q13. Describe the working of a heat engine with a neat labeled diagram. Define efficiency and derive the expression η = 1 – (Q₂/Q₁). Explain the significance of each term and discuss why real engines always have lower efficiency than the theoretical maximum.

Q14. A heat engine operates in a cycle, absorbing heat Q₁ from a source at temperature T₁ and rejecting heat Q₂ to a sink at temperature T₂.

(i) Draw the P-V diagram for a simple cyclic process.

(ii) Explain how the net work done is related to the area enclosed by the cycle.

(iii) If the engine absorbs 2000 J and rejects 1200 J, calculate the efficiency and work done.

(iv) What would be the maximum possible efficiency if T₁ = 600 K and T₂ = 300 K?

Q15. Consider two heat engines: Engine A operates between 800 K and 400 K with 40% efficiency, and Engine B operates between 600 K and 300 K with 35% efficiency.

(i) Calculate the Carnot efficiency for each engine.

(ii) Compare the actual efficiency to the Carnot efficiency for each.

(iii) Which engine is closer to being an ideal reversible engine?

(iv) What factors prevent real engines from achieving Carnot efficiency?

Q16. A heat engine operates between a source at 500 K and a sink at 300 K. In each cycle, it absorbs 1500 J of heat from the source.

(i) Calculate the maximum possible (Carnot) efficiency of this engine.

(ii) Calculate the maximum work that can be obtained per cycle.

(iii) If the actual efficiency is 60% of the Carnot efficiency, calculate the actual work done and heat rejected per cycle.

(iv) Calculate the actual heat rejected to the sink.

Q17. An automobile engine (petrol engine) operates in a cycle and has the following specifications:

Heat absorbed from combustion per cycle: 2000 J

Heat rejected to the exhaust per cycle: 1400 J

Number of cycles per second: 50

Calculate:

(i) The work done per cycle

(ii) The efficiency of the engine

(iii) The power output of the engine in watts

(iv) The total heat rejected per second

(v) If the fuel provides 4 × 10⁷ J per kg, and the engine consumes 0.5 kg of fuel per hour, calculate the overall efficiency of the engine.

Q18. A proposed heat engine design claims to operate between 400 K and 300 K with an efficiency of 30%. The designer says it uses a special working fluid that avoids the usual limitations.

(i) Calculate the Carnot efficiency for these temperatures.

(ii) Is the claimed efficiency possible? Justify your answer using the Second Law of Thermodynamics.

(iii) If the engine absorbs 1000 J per cycle, calculate the maximum work it can actually do.

(iv) What advice would you give to the designer?