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​ = 4.84 kWẆ = 1.1 kW

A refrigerator removes heat from its cold space at a rate of 4.84 kW while its compressor uses 1.1 kW of power. Find its coefficient of performance COPR.

Q̇L = 4.84 kWẆ = 1.1 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 33%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 50 MWη = 33%
Q̇L = MW
3.Medium
TH​ = 575 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 575 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 400 °CTL​ = ?EQH​ = 2500 kJQL​ = 1014 kJW

A reversible (Carnot) heat engine takes in 2500 kJ of heat from a reservoir at 400 °C and rejects 1014 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 400 °CQH = 2500 kJQL = 1014 kJ
TL = °C
5.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 32 °CTL = -10 °CQ̇L = 4 kW
Ẇmin = kW
6.Hard
TH​ = 800 °CT0​ = 30 °CTL​ = -10 °CERWQ̇H​ = 90 kWQ̇L​ = ?

A Carnot heat engine receives 90 kW of heat from a source at 800 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -10 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 800 °CT0 = 30 °CTL = -10 °CQ̇H = 90 kW
Q̇L = kW

Answer key

  1. 1. COPR = 4.4
  2. 2. Q̇L = 101.5 MW
  3. 3. ηmax = 63.08 %
  4. 4. TL = −0.1204 °C
  5. 5. Ẇmin = 0.6384 kW
  6. 6. Q̇L = 424.8 kW

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