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
kitchencold spaceRQ̇H​Q̇L​ = 9.03 kWẆ = 2.1 kW

A refrigerator removes heat from its cold space at a rate of 9.03 kW while its compressor uses 2.1 kW of power. Find its coefficient of performance COPR.

Q̇L = 9.03 kWẆ = 2.1 kW
COPR =
2.Easy
hot reservoircold reservoirEQH​ = 1900 kJQL​ = 1140 kJW

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1140 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 1900 kJQL = 1140 kJ
η = %
3.Medium
TH​ = 225 °CTL​ = ?EQH​ = 3600 kJQL​ = 2263 kJW

A reversible (Carnot) heat engine takes in 3600 kJ of heat from a reservoir at 225 °C and rejects 2263 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 225 °CQH = 3600 kJQL = 2263 kJ
TL = °C
4.Medium
TH​ = 275 °CTL​ = ?EQH​ = 3000 kJQL​ = 1632 kJW

A reversible (Carnot) heat engine takes in 3000 kJ of heat from a reservoir at 275 °C and rejects 1632 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 275 °CQH = 3000 kJQL = 1632 kJ
TL = °C
5.Hard
TH​ = 300 °CTL​ = 25 °CEQH​ = 900 kJQL​ = 639 kJW = 261 kJ

A heat engine takes in 900 kJ of heat from a reservoir at 300 °C, produces 261 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 300 °CTL = 25 °CQH = 900 kJW = 261 kJ
Sgen = kJ/K
6.Hard
TH​ = 21 °CTL​ = 5 °CHPQ̇H​ = 12 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 5 °C outside, delivering 12 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 5 °CQ̇H = 12 kW
Ẇmin = kW

Answer key

  1. 1. COPR = 4.3
  2. 2. η = 40 %
  3. 3. TL = 39.99 °C
  4. 4. TL = 25.04 °C
  5. 5. Sgen = 0.5729 kJ/K
  6. 6. Ẇmin = 0.6527 kW

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