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​ = 700 kJQL​ = 490 kJW = ?

A heat engine takes in 700 kJ of heat from a hot reservoir and rejects 490 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 700 kJQL = 490 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 55%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 55%
Q̇H = MW
3.Medium
TH​ = 675 °CTL​ = 25 °CEQH​ = 1400 kJQL​W = ?

A heat engine works between a hot reservoir at 675 °C and a cold reservoir at 25 °C. It takes in 1400 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 675 °CTL = 25 °CQH = 1400 kJ
Wmax = kJ
4.Medium
TH​ = 550 °CTL​ = ?EQH​ = 3400 kJQL​ = 1314 kJW

A reversible (Carnot) heat engine takes in 3400 kJ of heat from a reservoir at 550 °C and rejects 1314 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 550 °CQH = 3400 kJQL = 1314 kJ
TL = °C
5.Hard
1200 °CTm​ = ?10 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 1200 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 10 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 1200 °CTL = 10 °C
Tm = °C
6.Hard
TH​ = 21 °CTL​ = -5 °CHPQ̇H​ = 11 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is -5 °C outside, delivering 11 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = -5 °CQ̇H = 11 kW
COPmax =

Answer key

  1. 1. W = 210 kJ
  2. 2. Q̇H = 363.6 MW
  3. 3. Wmax = 959.8 kJ
  4. 4. TL = 44.97 °C
  5. 5. Tm = 372.7 °C
  6. 6. COPmax = 11.31

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