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​ = 14.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.7 delivers 14.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.7Q̇H = 14.5 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 1200 kJQL​ = 720 kJW = ?

A heat engine takes in 1200 kJ of heat from a hot reservoir and rejects 720 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1200 kJQL = 720 kJ
W = kJ
3.Medium
TH​ = 800 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 800 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 800 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 28 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 4.5 kWẆ

A reversible refrigerator keeps a cold room at -25 °C by removing 4.5 kW of heat, and rejects heat to the surroundings at 28 °C. Find the rate Q̇H at which it rejects heat.

TL = -25 °CTH = 28 °CQ̇L = 4.5 kW
Q̇H = kW
5.Hard
TH​ = 21 °CTL​ = 2 °CHPQ̇H​ = 14 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 21 °C while it is 2 °C outside, delivering 14 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 21 °CTL = 2 °CQ̇H = 14 kW
Ẇmin = kW
6.Hard
800 °CTm​ = ?35 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 800 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 35 °C. Both engines produce the same work. Find Tm in °C.

TH = 800 °CTL = 35 °C
Tm = °C

Answer key

  1. 1. Ẇ = 3.919 kW
  2. 2. W = 480 kJ
  3. 3. ηmax = 73.15 %
  4. 4. Q̇H = 5.461 kW
  5. 5. Ẇmin = 0.9043 kW
  6. 6. Tm = 417.5 °C

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