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​ = 4400 kJQL​ = 3080 kJW

A heat engine takes in 4400 kJ of heat from a hot reservoir and rejects 3080 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4400 kJQL = 3080 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 4100 kJQL​ = 2665 kJW = ?

A heat engine takes in 4100 kJ of heat from a hot reservoir and rejects 2665 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4100 kJQL = 2665 kJ
W = kJ
3.Medium
TH​ = 550 °CTL​ = 35 °CEQH​ = 3200 kJQL​W = ?

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 35 °C. It takes in 3200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 550 °CTL = 35 °CQH = 3200 kJ
Wmax = kJ
4.Medium
TH​ = 900 °CTL​ = 25 °CEQH​QL​η = 41%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 41%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 25 °Cη = 41%
ηII = %
5.Hard
TH​ = 55 °CTL​ = 7 °CHPQ̇H​ = 9 kWQ̇L​Ẇ = ?

A heat pump delivers 9 kW of heat to a heating system at 55 °C, taking heat from a source at 7 °C. Its actual COP is 55% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = 7 °CηII = 55%Q̇H = 9 kW
Ẇ = kW
6.Hard
TH​ = 30 °CTL​ = -18 °CRQ̇H​Q̇L​ = 1.5 kWẆ

A refrigerator keeps its cold space at -18 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 30 °CTL = -18 °CQ̇L = 1.5 kW
COPmax =

Answer key

  1. 1. η = 30 %
  2. 2. W = 1435 kJ
  3. 3. Wmax = 2002 kJ
  4. 4. ηII = 54.97 %
  5. 5. Ẇ = 2.394 kW
  6. 6. COPmax = 5.316

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