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​ = 8.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 2.7 delivers 8.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.7Q̇H = 8.5 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 16.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.7 delivers 16.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.7Q̇H = 16.5 kW
Q̇L = kW
3.Medium
TH​ = 550 °CTL​ = 40 °CEQH​ = 3800 kJQL​W = ?

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 40 °C. It takes in 3800 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 550 °CTL = 40 °CQH = 3800 kJ
Wmax = kJ
4.Medium
TH​ = 900 °CTL​ = 35 °CEQH​QL​η = 44%

A heat engine receives heat from a source at 900 °C and rejects heat to the surroundings at 35 °C. Its actual thermal efficiency is 44%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 900 °CTL = 35 °Cη = 44%
ηII = %
5.Hard
TH​ = 22 °CTL​ = 7 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is 7 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = 7 °CQ̇H = 14 kW
Ẇmin = kW
6.Hard
TH​ = 900 °CTL​ = 25 °CEQH​ = 4800 kJQL​ = 3024 kJW = 1776 kJ

A heat engine takes in 4800 kJ of heat from a reservoir at 900 °C, produces 1776 kJ of work and rejects the rest to a reservoir at 25 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 900 °CTL = 25 °CQH = 4800 kJW = 1776 kJ
Sgen = kJ/K

Answer key

  1. 1. Ẇ = 3.148 kW
  2. 2. Q̇L = 12.99 kW
  3. 3. Wmax = 2354 kJ
  4. 4. ηII = 59.67 %
  5. 5. Ẇmin = 0.7115 kW
  6. 6. Sgen = 6.051 kJ/K

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