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
kitchencold spaceRQ̇H​Q̇L​ = 3.78 kWẆ = 1.8 kW

A refrigerator removes heat from its cold space at a rate of 3.78 kW while its compressor uses 1.8 kW of power. Find its coefficient of performance COPR.

Q̇L = 3.78 kWẆ = 1.8 kW
COPR =
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 300 MW

A power plant delivers a net power output of 300 MW with a thermal efficiency of 40%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 300 MWη = 40%
Q̇H = MW
3.Medium
TH​ = 600 °CTL​ = 25 °CEQH​ = 600 kJQL​W = ?

A heat engine works between a hot reservoir at 600 °C and a cold reservoir at 25 °C. It takes in 600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 600 °CTL = 25 °CQH = 600 kJ
Wmax = kJ
4.Medium
TH​ = 250 °CTL​ = ?EQH​ = 1000 kJQL​ = 522 kJW

A reversible (Carnot) heat engine takes in 1000 kJ of heat from a reservoir at 250 °C and rejects 522 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 250 °CQH = 1000 kJQL = 522 kJ
TL = °C
5.Hard
TH​ = 500 °CTL​ = 15 °CEQH​ = 1600 kJQL​ = 1104 kJW = 496 kJ

A heat engine takes in 1600 kJ of heat from a reservoir at 500 °C, produces 496 kJ of work and rejects the rest to a reservoir at 15 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 500 °CTL = 15 °CQH = 1600 kJW = 496 kJ
Sgen = kJ/K
6.Hard
600 °CTm​ = ?20 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 600 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 20 °C. Both engines produce the same work. Find Tm in °C.

TH = 600 °CTL = 20 °C
Tm = °C

Answer key

  1. 1. COPR = 2.1
  2. 2. Q̇H = 750 MW
  3. 3. Wmax = 395.1 kJ
  4. 4. TL = −0.0657 °C
  5. 5. Sgen = 1.762 kJ/K
  6. 6. Tm = 310 °C

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