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​ = 2400 kJQL​ = 1680 kJW

A heat engine takes in 2400 kJ of heat from a hot reservoir and rejects 1680 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 2400 kJQL = 1680 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 1900 kJQL​ = 1235 kJW = ?

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1235 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1900 kJQL = 1235 kJ
W = kJ
3.Medium
TH​ = 525 °CTL​ = 30 °CEQH​ = 1500 kJQL​W = ?

A heat engine works between a hot reservoir at 525 °C and a cold reservoir at 30 °C. It takes in 1500 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 525 °CTL = 30 °CQH = 1500 kJ
Wmax = kJ
4.Medium
TH​ = 600 °CTL​ = ?EQH​ = 3200 kJQL​ = 1184 kJW

A reversible (Carnot) heat engine takes in 3200 kJ of heat from a reservoir at 600 °C and rejects 1184 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 600 °CQH = 3200 kJQL = 1184 kJ
TL = °C
5.Hard
TH​ = 35 °CTL​ = -25 °CRQ̇H​Q̇L​ = 1 kWẆ = ?

A refrigerator keeps its cold space at -25 °C in a kitchen at 35 °C, removing heat from the cold space at 1 kW. Find the minimum power input Ẇmin.

TH = 35 °CTL = -25 °CQ̇L = 1 kW
Ẇmin = kW
6.Hard
TH​ = 900 °CT0​ = 20 °CTL​ = -20 °CERWQ̇H​ = 140 kWQ̇L​ = ?

A Carnot heat engine receives 140 kW of heat from a source at 900 °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 -20 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 900 °CT0 = 20 °CTL = -20 °CQ̇H = 140 kW
Q̇L = kW

Answer key

  1. 1. η = 30 %
  2. 2. W = 665 kJ
  3. 3. Wmax = 930.3 kJ
  4. 4. TL = 49.92 °C
  5. 5. Ẇmin = 0.2418 kW
  6. 6. Q̇L = 664.6 kW

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