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 1300 kJ of heat from a hot reservoir and rejects 780 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 1300 kJQ_L = 780 kJ

η = %

2.Easy

A heat engine takes in 1400 kJ of heat from a hot reservoir and rejects 1120 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

Q_H = 1400 kJQ_L = 1120 kJ

η = %

3.Medium

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency η_max.

T_H = 250 °CT_L = 15 °C

η_max = %

4.Medium

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 20 °C. Find the highest possible thermal efficiency η_max.

T_H = 575 °CT_L = 20 °C

η_max = %

5.Hard

A heat pump delivers 11 kW of heat to a heating system at 55 °C, taking heat from a source at -5 °C. Its actual COP is 40% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

T_H = 55 °CT_L = -5 °Cη_II = 40%Q̇_H = 11 kW

Ẇ = kW

6.Hard

Two Carnot engines work in series. Engine A receives heat from a reservoir at 900 °C and rejects heat to an intermediate reservoir at temperature T_m. Engine B takes all that heat and rejects heat to a reservoir at 20 °C. Both engines produce the same work. Find T_m in °C.

T_H = 900 °CT_L = 20 °C

T_m = °C

Answer key

1. η = 40 %
2. η = 20 %
3. η_max = 44.92 %
4. η_max = 65.44 %
5. Ẇ = 5.028 kW
6. T_m = 460 °C

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