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
hot reservoircold reservoirEQH​ = 2800 kJQL​ = 1680 kJW = ?

A heat engine takes in 2800 kJ of heat from a hot reservoir and rejects 1680 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2800 kJQL = 1680 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 30%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 300 MWη = 30%
Q̇H = MW
3.Medium
TH​ = 600 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 600 °CTL = 10 °C
ηmax = %
4.Medium
TH​ = 575 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 575 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 575 °CTL = 40 °C
ηmax = %
5.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 6 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 6 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = -5 °CQ̇H = 6 kW
Ẇmin = kW
6.Hard
TH​ = 45 °CTL​ = 0 °CHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump delivers 15 kW of heat to a heating system at 45 °C, taking heat from a source at 0 °C. Its actual COP is 50% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = 0 °CηII = 50%Q̇H = 15 kW
Ẇ = kW

Answer key

  1. 1. W = 1120 kJ
  2. 2. Q̇H = 1000 MW
  3. 3. ηmax = 67.57 %
  4. 4. ηmax = 63.08 %
  5. 5. Ẇmin = 0.5303 kW
  6. 6. Ẇ = 4.243 kW

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