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​ = 1820 kJW = ?

A heat engine takes in 2800 kJ of heat from a hot reservoir and rejects 1820 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2800 kJQL = 1820 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 50 MW

A power plant delivers a net power output of 50 MW with a thermal efficiency of 25%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 50 MWη = 25%
Q̇H = MW
3.Medium
TH​ = 700 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 700 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 700 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 600 °CTL​ = 5 °CEQH​ = 4100 kJQL​W = ?

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 5 °C. It takes in 4100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 600 °CTL = 5 °CQH = 4100 kJ
Wmax = kJ
5.Hard
TH​ = 28 °CTL​ = 5 °CRQ̇H​Q̇L​ = 4 kWẆ

A refrigerator keeps its cold space at 5 °C in a kitchen at 28 °C, removing heat from the cold space at 4 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = 5 °CQ̇L = 4 kW
COPmax =
6.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 10 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 10 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 20 °CTL = 0 °CQ̇H = 10 kW
Ẇmin = kW

Answer key

  1. 1. W = 980 kJ
  2. 2. Q̇H = 200 MW
  3. 3. ηmax = 68.33 %
  4. 4. Wmax = 2794 kJ
  5. 5. COPmax = 12.09
  6. 6. Ẇmin = 0.6822 kW

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