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​ = 1100 kJQL​ = 605 kJW

A heat engine takes in 1100 kJ of heat from a hot reservoir and rejects 605 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1100 kJQL = 605 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 50%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 100 MWη = 50%
Q̇H = MW
3.Medium
TH​ = 325 °CTL​ = 40 °CEQH​ = 2600 kJQL​W = ?

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 40 °C. It takes in 2600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 325 °CTL = 40 °CQH = 2600 kJ
Wmax = kJ
4.Medium
TH​ = 300 °CTL​ = 30 °CEQH​ = 600 kJQL​W = ?

A heat engine works between a hot reservoir at 300 °C and a cold reservoir at 30 °C. It takes in 600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 300 °CTL = 30 °CQH = 600 kJ
Wmax = kJ
5.Hard
TH​ = 28 °CTL​ = -18 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 28 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = -18 °CQ̇L = 4 kW
Ẇmin = kW
6.Hard
TH​ = 800 °CT0​ = 30 °CTL​ = -25 °CERWQ̇H​ = 80 kWQ̇L​ = ?

A Carnot heat engine receives 80 kW of heat from a source at 800 °C and rejects heat to the surroundings at 30 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -25 °C and also rejects heat to the surroundings at 30 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 800 °CT0 = 30 °CTL = -25 °CQ̇H = 80 kW
Q̇L = kW

Answer key

  1. 1. η = 45 %
  2. 2. Q̇H = 200 MW
  3. 3. Wmax = 1239 kJ
  4. 4. Wmax = 282.6 kJ
  5. 5. Ẇmin = 0.7211 kW
  6. 6. Q̇L = 259 kW

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