Heat engines & refrigerators worksheet with answers

Free printable Heat engines & refrigerators worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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1.Easy

A heat engine takes in 1700 kJ of heat from a hot reservoir and rejects 1360 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 1700 kJQ_L = 1360 kJ

η = %

2.Easy

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2535 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 3900 kJQ_L = 2535 kJ

η = %

3.Medium

A reversible (Carnot) heat engine takes in 4400 kJ of heat from a reservoir at 525 °C and rejects 1837 kJ per cycle. Find the temperature T_L of the cold reservoir in °C.

T_H = 525 °CQ_H = 4400 kJQ_L = 1837 kJ

T_L = °C

4.Medium

A reversible refrigerator keeps a cold room at 4 °C by removing 8.5 kW of heat, and rejects heat to the surroundings at 25 °C. Find the rate Q̇_H at which it rejects heat.

T_L = 4 °CT_H = 25 °CQ̇_L = 8.5 kW

Q̇_H = kW

5.Hard

A heat engine takes in 1400 kJ of heat from a reservoir at 500 °C, produces 448 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated S_gen per cycle.

T_H = 500 °CT_L = 10 °CQ_H = 1400 kJW = 448 kJ

S_gen = kJ/K

6.Hard

A refrigerator keeps its cold space at -20 °C in a kitchen at 32 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇ_min.

T_H = 32 °CT_L = -20 °CQ̇_L = 1.5 kW

Ẇ_min = kW

Answer key

1. η = 20 %
2. η = 35 %
3. T_L = 60.08 °C
4. Q̇_H = 9.144 kW
5. S_gen = 1.551 kJ/K
6. Ẇ_min = 0.3081 kW

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