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​ = 5.2 kWẆ = 1.3 kW

A refrigerator removes heat from its cold space at a rate of 5.2 kW while its compressor uses 1.3 kW of power. Find its coefficient of performance COPR.

Q̇L = 5.2 kWẆ = 1.3 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 400 MW

A power plant delivers a net power output of 400 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 400 MWη = 25%
Q̇L = MW
3.Medium
TH​ = 450 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 450 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 30 °CTL​ = 0 °CRQ̇H​ = ?Q̇L​ = 8.5 kWẆ

A reversible refrigerator keeps a cold room at 0 °C by removing 8.5 kW of heat, and rejects heat to the surroundings at 30 °C. Find the rate Q̇H at which it rejects heat.

TL = 0 °CTH = 30 °CQ̇L = 8.5 kW
Q̇H = kW
5.Hard
TH​ = 35 °CTL​ = -18 °CRQ̇H​Q̇L​ = 4 kWẆ

A refrigerator keeps its cold space at -18 °C in a kitchen at 35 °C, removing heat from the cold space at 4 kW. Find the highest possible coefficient of performance COPmax.

TH = 35 °CTL = -18 °CQ̇L = 4 kW
COPmax =
6.Hard
TH​ = 30 °CTL​ = -25 °CRQ̇H​Q̇L​ = 3 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 30 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -25 °CQ̇L = 3 kW
Ẇmin = kW

Answer key

  1. 1. COPR = 4
  2. 2. Q̇L = 1200 MW
  3. 3. ηmax = 56.7 %
  4. 4. Q̇H = 9.434 kW
  5. 5. COPmax = 4.814
  6. 6. Ẇmin = 0.6649 kW

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