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​ = 2800 kJQL​ = 2100 kJW = ?

A heat engine takes in 2800 kJ of heat from a hot reservoir and rejects 2100 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2800 kJQL = 2100 kJ
W = kJ
2.Easy
hot reservoircold reservoirEQH​ = 1900 kJQL​ = 1330 kJW

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1330 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1900 kJQL = 1330 kJ
η = %
3.Medium
TH​ = 675 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 675 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 675 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 250 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 35 °C
ηmax = %
5.Hard
TH​ = 32 °CTL​ = 4 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at 4 °C in a kitchen at 32 °C, removing heat from the cold space at 2.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = 4 °CQ̇L = 2.5 kW
COPmax =
6.Hard
TH​ = 650 °CT0​ = 20 °CTL​ = -30 °CERWQ̇H​ = 180 kWQ̇L​ = ?

A Carnot heat engine receives 180 kW of heat from a source at 650 °C and rejects heat to the surroundings at 20 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -30 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 650 °CT0 = 20 °CTL = -30 °CQ̇H = 180 kW
Q̇L = kW

Answer key

  1. 1. W = 700 kJ
  2. 2. η = 30 %
  3. 3. ηmax = 70.66 %
  4. 4. ηmax = 41.1 %
  5. 5. COPmax = 9.898
  6. 6. Q̇L = 597.4 kW

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