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
hot reservoircold reservoirEQH​ = 1600 kJQL​ = 880 kJW

A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 880 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1600 kJQL = 880 kJ
η = %
2.Easy
houseoutside airHPQ̇H​ = 13.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.6 delivers 13.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.6Q̇H = 13.5 kW
Q̇L = kW
3.Medium
TH​ = 800 °CTL​ = 30 °CEQH​QL​η = 29%

A heat engine receives heat from a source at 800 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 29%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 800 °CTL = 30 °Cη = 29%
ηII = %
4.Medium
TH​ = 800 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 35 °C
ηmax = %
5.Hard
TH​ = 600 °CTL​ = 35 °CEQH​ = 4700 kJQL​ = 2256 kJW = 2444 kJ

A heat engine takes in 4700 kJ of heat from a reservoir at 600 °C, produces 2444 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 600 °CTL = 35 °CQH = 4700 kJW = 2444 kJ
Sgen = kJ/K
6.Hard
TH​ = 30 °CTL​ = -18 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -18 °CQ̇L = 1.5 kW
Ẇmin = kW

Answer key

  1. 1. η = 45 %
  2. 2. Q̇L = 10.57 kW
  3. 3. ηII = 40.42 %
  4. 4. ηmax = 71.29 %
  5. 5. Sgen = 1.938 kJ/K
  6. 6. Ẇmin = 0.2822 kW

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