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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 33%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 100 MWη = 33%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 4900 kJQL​ = 2940 kJW = ?

A heat engine takes in 4900 kJ of heat from a hot reservoir and rejects 2940 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 4900 kJQL = 2940 kJ
W = kJ
3.Medium
TH​ = 375 °CTL​ = ?EQH​ = 1500 kJQL​ = 644 kJW

A reversible (Carnot) heat engine takes in 1500 kJ of heat from a reservoir at 375 °C and rejects 644 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 375 °CQH = 1500 kJQL = 644 kJ
TL = °C
4.Medium
TH​ = 350 °CTL​ = 25 °CEQH​QL​η = 39%

A heat engine receives heat from a source at 350 °C and rejects heat to the surroundings at 25 °C. Its actual thermal efficiency is 39%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 350 °CTL = 25 °Cη = 39%
ηII = %
5.Hard
TH​ = 1000 °CT0​ = 20 °CTL​ = -5 °CERWQ̇H​ = 60 kWQ̇L​ = ?

A Carnot heat engine receives 60 kW of heat from a source at 1000 °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 -5 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 1000 °CT0 = 20 °CTL = -5 °CQ̇H = 60 kW
Q̇L = kW
6.Hard
TH​ = 28 °CTL​ = -10 °CRQ̇H​Q̇L​ = 2 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 28 °C, removing heat from the cold space at 2 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = -10 °CQ̇L = 2 kW
COPmax =

Answer key

  1. 1. Q̇H = 303 MW
  2. 2. W = 1960 kJ
  3. 3. TL = 5.122 °C
  4. 4. ηII = 74.78 %
  5. 5. Q̇L = 495.4 kW
  6. 6. COPmax = 6.925

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