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 = 750 MW

A power plant delivers a net power output of 750 MW with a thermal efficiency of 50%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 750 MWη = 50%
Q̇H = MW
2.Easy
hot reservoircold reservoirEQH​ = 2000 kJQL​ = 1200 kJW = ?

A heat engine takes in 2000 kJ of heat from a hot reservoir and rejects 1200 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2000 kJQL = 1200 kJ
W = kJ
3.Medium
TH​ = 200 °CTL​ = ?EQH​ = 3400 kJQL​ = 2035 kJW

A reversible (Carnot) heat engine takes in 3400 kJ of heat from a reservoir at 200 °C and rejects 2035 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 200 °CQH = 3400 kJQL = 2035 kJ
TL = °C
4.Medium
TH​ = 650 °CTL​ = 40 °CEQH​QL​η = 40%

A heat engine receives heat from a source at 650 °C and rejects heat to the surroundings at 40 °C. Its actual thermal efficiency is 40%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 650 °CTL = 40 °Cη = 40%
ηII = %
5.Hard
TH​ = 20 °CTL​ = 0 °CHPQ̇H​ = 8 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is 0 °C outside, delivering 8 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = 0 °CQ̇H = 8 kW
COPmax =
6.Hard
650 °CTm​ = ?35 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 650 °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 = 650 °CTL = 35 °C
Tm = °C

Answer key

  1. 1. Q̇H = 1500 MW
  2. 2. W = 800 kJ
  3. 3. TL = 10.04 °C
  4. 4. ηII = 60.53 %
  5. 5. COPmax = 14.66
  6. 6. Tm = 342.5 °C

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