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​ = 1200 kJW = ?

A heat engine takes in 1600 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 = 1600 kJQL = 1200 kJ
W = kJ
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 500 MW

A power plant delivers a net power output of 500 MW with a thermal efficiency of 45%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 500 MWη = 45%
Q̇H = MW
3.Medium
TH​ = 20 °CTL​ = -30 °CRQ̇H​ = ?Q̇L​ = 4 kWẆ

A reversible refrigerator keeps a cold room at -30 °C by removing 4 kW of heat, and rejects heat to the surroundings at 20 °C. Find the rate Q̇H at which it rejects heat.

TL = -30 °CTH = 20 °CQ̇L = 4 kW
Q̇H = kW
4.Medium
TH​ = 650 °CTL​ = 30 °CEQH​ = 4000 kJQL​W = ?

A heat engine works between a hot reservoir at 650 °C and a cold reservoir at 30 °C. It takes in 4000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 650 °CTL = 30 °CQH = 4000 kJ
Wmax = kJ
5.Hard
700 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 700 °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 = 700 °CTL = 40 °C
Tm = °C
6.Hard
TH​ = 700 °CTL​ = 35 °CEQH​ = 1000 kJQL​ = 450 kJW = 550 kJ

A heat engine takes in 1000 kJ of heat from a reservoir at 700 °C, produces 550 kJ of work and rejects the rest to a reservoir at 35 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 700 °CTL = 35 °CQH = 1000 kJW = 550 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 400 kJ
  2. 2. Q̇H = 1111 MW
  3. 3. Q̇H = 4.823 kW
  4. 4. Wmax = 2686 kJ
  5. 5. Tm = 278.9 °C
  6. 6. Sgen = 0.4327 kJ/K

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