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 3100 kJ of heat from a hot reservoir and rejects 2170 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 3100 kJQ_L = 2170 kJ

η = %

2.Easy

A heat engine takes in 3700 kJ of heat from a hot reservoir and rejects 2960 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 3700 kJQ_L = 2960 kJ

η = %

3.Medium

A heat engine works between a hot reservoir at 775 °C and a cold reservoir at 25 °C. Find the highest possible thermal efficiency η_max.

T_H = 775 °CT_L = 25 °C

η_max = %

4.Medium

A heat engine works between a hot reservoir at 425 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency η_max.

T_H = 425 °CT_L = 15 °C

η_max = %

5.Hard

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

T_H = 21 °CT_L = -5 °CQ̇_H = 5 kW

Ẇ_min = kW

6.Hard

A Carnot heat engine receives 180 kW of heat from a source at 750 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -15 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇_L at which heat is removed from the freezer.

T_H = 750 °CT₀ = 20 °CT_L = -15 °CQ̇_H = 180 kW

Q̇_L = kW

Answer key

1. η = 30 %
2. η = 20 %
3. η_max = 71.55 %
4. η_max = 58.73 %
5. Ẇ_min = 0.442 kW
6. Q̇_L = 947.2 kW

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