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​ = 7 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.1 delivers 7 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.1Q̇H = 7 kW
Ẇ = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 40%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 150 MWη = 40%
Q̇H = MW
3.Medium
TH​ = 625 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 625 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 775 °CTL​ = ?EQH​ = 3000 kJQL​ = 853 kJW

A reversible (Carnot) heat engine takes in 3000 kJ of heat from a reservoir at 775 °C and rejects 853 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 775 °CQH = 3000 kJQL = 853 kJ
TL = °C
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 12 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 12 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = -10 °CQ̇H = 12 kW
COPmax =
6.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 7 °CQ̇H = 6 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 1.707 kW
  2. 2. Q̇H = 375 MW
  3. 3. ηmax = 65.69 %
  4. 4. TL = 24.87 °C
  5. 5. COPmax = 9.489
  6. 6. Ẇmin = 0.3049 kW

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