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​ = 4.86 kWẆ = 1.8 kW

A refrigerator removes heat from its cold space at a rate of 4.86 kW while its compressor uses 1.8 kW of power. Find its coefficient of performance COPR.

Q̇L = 4.86 kWẆ = 1.8 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 600 MW

A power plant delivers a net power output of 600 MW with a thermal efficiency of 50%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 600 MWη = 50%
Q̇L = MW
3.Medium
TH​ = 450 °CTL​ = 30 °CEQH​QL​η = 44%

A heat engine receives heat from a source at 450 °C and rejects heat to the surroundings at 30 °C. Its actual thermal efficiency is 44%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 450 °CTL = 30 °Cη = 44%
ηII = %
4.Medium
TH​ = 450 °CTL​ = 25 °CEQH​ = 3700 kJQL​W = ?

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 25 °C. It takes in 3700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 450 °CTL = 25 °CQH = 3700 kJ
Wmax = kJ
5.Hard
TH​ = 35 °CTL​ = -18 °CRQ̇H​Q̇L​ = 4.5 kWẆ

A refrigerator keeps its cold space at -18 °C in a kitchen at 35 °C, removing heat from the cold space at 4.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 35 °CTL = -18 °CQ̇L = 4.5 kW
COPmax =
6.Hard
TH​ = 25 °CTL​ = 2 °CRQ̇H​Q̇L​ = 2.5 kWẆ = ?

A refrigerator keeps its cold space at 2 °C in a kitchen at 25 °C, removing heat from the cold space at 2.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 2 °CQ̇L = 2.5 kW
Ẇmin = kW

Answer key

  1. 1. COPR = 2.7
  2. 2. Q̇L = 600 MW
  3. 3. ηII = 75.76 %
  4. 4. Wmax = 2175 kJ
  5. 5. COPmax = 4.814
  6. 6. Ẇmin = 0.209 kW

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