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
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 1000 MW

A power plant delivers a net power output of 1000 MW with a thermal efficiency of 25%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 1000 MWη = 25%
Q̇H = MW
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 400 MW

A power plant delivers a net power output of 400 MW with a thermal efficiency of 25%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 400 MWη = 25%
Q̇L = MW
3.Medium
TH​ = 575 °CTL​ = ?EQH​ = 2300 kJQL​ = 795 kJW

A reversible (Carnot) heat engine takes in 2300 kJ of heat from a reservoir at 575 °C and rejects 795 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 575 °CQH = 2300 kJQL = 795 kJ
TL = °C
4.Medium
TH​ = 450 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 450 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 450 °CTL = 5 °C
ηmax = %
5.Hard
TH​ = 55 °CTL​ = -5 °CHPQ̇H​ = 8 kWQ̇L​Ẇ = ?

A heat pump delivers 8 kW of heat to a heating system at 55 °C, taking heat from a source at -5 °C. Its actual COP is 30% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 55 °CTL = -5 °CηII = 30%Q̇H = 8 kW
Ẇ = kW
6.Hard
TH​ = 20 °CTL​ = 2 °CHPQ̇H​ = 9 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is 2 °C outside, delivering 9 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = 2 °CQ̇H = 9 kW
COPmax =

Answer key

  1. 1. Q̇H = 4000 MW
  2. 2. Q̇L = 1200 MW
  3. 3. TL = 20.01 °C
  4. 4. ηmax = 61.54 %
  5. 5. Ẇ = 4.876 kW
  6. 6. COPmax = 16.29

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