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
kitchencold spaceRQ̇H​Q̇L​ = 2.22 kWẆ = 0.6 kW

A refrigerator removes heat from its cold space at a rate of 2.22 kW while its compressor uses 0.6 kW of power. Find its coefficient of performance COPR.

Q̇L = 2.22 kWẆ = 0.6 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 38%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 38%
Q̇H = MW
3.Medium
TH​ = 200 °CTL​ = 30 °CEQH​QL​W

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 30 °C. Find the highest possible thermal efficiency ηmax.

TH = 200 °CTL = 30 °C
ηmax = %
4.Medium
TH​ = 900 °CTL​ = 30 °CEQH​QL​η = 52%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 52%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 30 °Cη = 52%
ηII = %
5.Hard
TH​ = 25 °CTL​ = 5 °CRQ̇H​Q̇L​ = 3.5 kWẆ = ?

A refrigerator keeps its cold space at 5 °C in a kitchen at 25 °C, removing heat from the cold space at 3.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 5 °CQ̇L = 3.5 kW
Ẇmin = kW
6.Hard
TH​ = 750 °CTL​ = 35 °CEQH​ = 1800 kJQL​ = 1044 kJW = 756 kJ

A heat engine takes in 1800 kJ of heat from a reservoir at 750 °C, produces 756 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 750 °CTL = 35 °CQH = 1800 kJW = 756 kJ
Sgen = kJ/K

Answer key

  1. 1. COPR = 3.7
  2. 2. Q̇H = 1974 MW
  3. 3. ηmax = 35.93 %
  4. 4. ηII = 70.12 %
  5. 5. Ẇmin = 0.2517 kW
  6. 6. Sgen = 1.629 kJ/K

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