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
hot reservoircold reservoirEQH​ = 3600 kJQL​ = 2700 kJW

A heat engine takes in 3600 kJ of heat from a hot reservoir and rejects 2700 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3600 kJQL = 2700 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 55%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 55%
Q̇H = MW
3.Medium
TH​ = 600 °CTL​ = 10 °CEQH​QL​η = 27%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 27%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 10 °Cη = 27%
ηII = %
4.Medium
TH​ = 625 °CTL​ = ?EQH​ = 2200 kJQL​ = 669 kJW

A reversible (Carnot) heat engine takes in 2200 kJ of heat from a reservoir at 625 °C and rejects 669 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 625 °CQH = 2200 kJQL = 669 kJ
TL = °C
5.Hard
TH​ = 55 °CTL​ = 10 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump delivers 12 kW of heat to a heating system at 55 °C, taking heat from a source at 10 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 10 °CηII = 30%Q̇H = 12 kW
Ẇ = kW
6.Hard
TH​ = 25 °CTL​ = 2 °CRQ̇H​Q̇L​ = 3 kWẆ = ?

A refrigerator keeps its cold space at 2 °C in a kitchen at 25 °C, removing heat from the cold space at 3 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = 2 °CQ̇L = 3 kW
Ẇmin = kW

Answer key

  1. 1. η = 25 %
  2. 2. Q̇H = 1364 MW
  3. 3. ηII = 39.96 %
  4. 4. TL = −0.03075 °C
  5. 5. Ẇ = 5.485 kW
  6. 6. Ẇmin = 0.2508 kW

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