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
houseoutside airHPQ̇H​ = 9.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 2.9 delivers 9.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 2.9Q̇H = 9.5 kW
Q̇L = kW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 35%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 35%
Q̇L = MW
3.Medium
TH​ = 550 °CTL​ = 10 °CEQH​QL​η = 39%

A heat engine receives heat from a source at 550 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 39%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 550 °CTL = 10 °Cη = 39%
ηII = %
4.Medium
TH​ = 850 °CTL​ = 15 °CEQH​QL​η = 48%

A heat engine receives heat from a source at 850 °C and rejects heat to the surroundings at 15 °C. Its actual thermal efficiency is 48%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 850 °CTL = 15 °Cη = 48%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 10 °CHPQ̇H​ = 19.5 kWQ̇L​Ẇ = ?

A heat pump delivers 19.5 kW of heat to a heating system at 22 °C, taking heat from a source at 10 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 22 °CTL = 10 °CηII = 50%Q̇H = 19.5 kW
Ẇ = kW
6.Hard
750 °CTm​ = ?30 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 750 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 30 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 750 °CTL = 30 °C
Tm = °C

Answer key

  1. 1. Q̇L = 6.224 kW
  2. 2. Q̇L = 371.4 MW
  3. 3. ηII = 59.45 %
  4. 4. ηII = 64.56 %
  5. 5. Ẇ = 1.586 kW
  6. 6. Tm = 283.8 °C

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