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
houseoutside airHPQ̇H​ = 17.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4 delivers 17.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4Q̇H = 17.5 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 1400 kJQL​ = 1120 kJW = ?

A heat engine takes in 1400 kJ of heat from a hot reservoir and rejects 1120 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1400 kJQL = 1120 kJ
W = kJ
3.Medium
TH​ = 400 °CTL​ = ?EQH​ = 3300 kJQL​ = 1486 kJW

A reversible (Carnot) heat engine takes in 3300 kJ of heat from a reservoir at 400 °C and rejects 1486 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 400 °CQH = 3300 kJQL = 1486 kJ
TL = °C
4.Medium
TH​ = 225 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 225 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 225 °CTL = 15 °C
ηmax = %
5.Hard
TH​ = 30 °CTL​ = 4 °CRQ̇H​Q̇L​ = 2 kWẆ = ?

A refrigerator keeps its cold space at 4 °C in a kitchen at 30 °C, removing heat from the cold space at 2 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = 4 °CQ̇L = 2 kW
Ẇmin = kW
6.Hard
TH​ = 450 °CT0​ = 20 °CTL​ = 0 °CERWQ̇H​ = 140 kWQ̇L​ = ?

A Carnot heat engine receives 140 kW of heat from a source at 450 °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 0 °C and also rejects heat to the surroundings at 20 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 450 °CT0 = 20 °CTL = 0 °CQ̇H = 140 kW
Q̇L = kW

Answer key

  1. 1. Ẇ = 4.375 kW
  2. 2. W = 280 kJ
  3. 3. TL = 29.97 °C
  4. 4. ηmax = 42.16 %
  5. 5. Ẇmin = 0.1876 kW
  6. 6. Q̇L = 1137 kW

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