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
houseoutside airHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.9 delivers 15 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.9Q̇H = 15 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 1000 kJQL​ = 650 kJW = ?

A heat engine takes in 1000 kJ of heat from a hot reservoir and rejects 650 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1000 kJQL = 650 kJ
W = kJ
3.Medium
TH​ = 25 °CTL​ = -25 °CRQ̇H​ = ?Q̇L​ = 5.5 kWẆ

A reversible refrigerator keeps a cold room at -25 °C by removing 5.5 kW of heat, and rejects heat to the surroundings at 25 °C. Find the rate Q̇H at which it rejects heat.

TL = -25 °CTH = 25 °CQ̇L = 5.5 kW
Q̇H = kW
4.Medium
TH​ = 250 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 250 °CTL = 15 °C
ηmax = %
5.Hard
500 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 500 °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 = 500 °CTL = 40 °C
Tm = °C
6.Hard
TH​ = 350 °CTL​ = 20 °CEQH​ = 3600 kJQL​ = 2664 kJW = 936 kJ

A heat engine takes in 3600 kJ of heat from a reservoir at 350 °C, produces 936 kJ of work and rejects the rest to a reservoir at 20 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 350 °CTL = 20 °CQH = 3600 kJW = 936 kJ
Sgen = kJ/K

Answer key

  1. 1. Ẇ = 3.061 kW
  2. 2. W = 350 kJ
  3. 3. Q̇H = 6.608 kW
  4. 4. ηmax = 44.92 %
  5. 5. Tm = 218.9 °C
  6. 6. Sgen = 3.31 kJ/K

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