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 1100 kJ of heat from a hot reservoir and rejects 770 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 1100 kJQ_L = 770 kJ

η = %

2.Easy

A heat engine takes in 900 kJ of heat from a hot reservoir and rejects 720 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 900 kJQ_L = 720 kJ

η = %

3.Medium

A reversible (Carnot) heat engine takes in 3700 kJ of heat from a reservoir at 475 °C and rejects 1351 kJ per cycle. Find the temperature T_L of the cold reservoir in °C.

T_H = 475 °CQ_H = 3700 kJQ_L = 1351 kJ

T_L = °C

4.Medium

A heat engine receives heat from a source at 750 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 50%. Find its second-law efficiency η_II, the ratio of the actual efficiency to the Carnot efficiency.

T_H = 750 °CT_L = 25 °Cη = 50%

η_II = %

5.Hard

A heat pump keeps a house at 21 °C while it is 5 °C outside, delivering 12 kW of heat to the house. Find the minimum power input Ẇ_min.

T_H = 21 °CT_L = 5 °CQ̇_H = 12 kW

Ẇ_min = kW

6.Hard

A refrigerator keeps its cold space at -10 °C in a kitchen at 25 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇ_min.

T_H = 25 °CT_L = -10 °CQ̇_L = 3 kW

Ẇ_min = kW

Answer key

1. η = 30 %
2. η = 20 %
3. T_L = 0.02585 °C
4. η_II = 70.56 %
5. Ẇ_min = 0.6527 kW
6. Ẇ_min = 0.399 kW

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