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​ = 1600 kJQL​ = 960 kJW = ?

A heat engine takes in 1600 kJ of heat from a hot reservoir and rejects 960 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1600 kJQL = 960 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 33%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 200 MWη = 33%
Q̇L = MW
3.Medium
TH​ = 350 °CTL​ = 10 °CEQH​QL​W

A heat engine works between a hot reservoir at 350 °C and a cold reservoir at 10 °C. Find the highest possible thermal efficiency ηmax.

TH = 350 °CTL = 10 °C
ηmax = %
4.Medium
TH​ = 550 °CTL​ = 5 °CEQH​ = 1200 kJQL​W = ?

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 5 °C. It takes in 1200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 550 °CTL = 5 °CQH = 1200 kJ
Wmax = kJ
5.Hard
TH​ = 650 °CTL​ = 20 °CEQH​ = 4400 kJQL​ = 2904 kJW = 1496 kJ

A heat engine takes in 4400 kJ of heat from a reservoir at 650 °C, produces 1496 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 650 °CTL = 20 °CQH = 4400 kJW = 1496 kJ
Sgen = kJ/K
6.Hard
850 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 850 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 40 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 850 °CTL = 40 °C
Tm = °C

Answer key

  1. 1. W = 640 kJ
  2. 2. Q̇L = 406.1 MW
  3. 3. ηmax = 54.56 %
  4. 4. Wmax = 794.5 kJ
  5. 5. Sgen = 5.14 kJ/K
  6. 6. Tm = 319.9 °C

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