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​ = 6 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.8 delivers 6 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.8Q̇H = 6 kW
Ẇ = kW
2.Easy
houseoutside airHPQ̇H​ = 16 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 2.8 delivers 16 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 2.8Q̇H = 16 kW
Q̇L = kW
3.Medium
TH​ = 725 °CTL​ = 15 °CEQH​QL​W

A heat engine works between a hot reservoir at 725 °C and a cold reservoir at 15 °C. Find the highest possible thermal efficiency ηmax.

TH = 725 °CTL = 15 °C
ηmax = %
4.Medium
TH​ = 35 °CTL​ = 5 °CRQ̇H​ = ?Q̇L​ = 2.5 kWẆ

A reversible refrigerator keeps a cold room at 5 °C by removing 2.5 kW of heat, and rejects heat to the surroundings at 35 °C. Find the rate Q̇H at which it rejects heat.

TL = 5 °CTH = 35 °CQ̇L = 2.5 kW
Q̇H = kW
5.Hard
700 °CTm​ = ?15 °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 15 °C. Both engines have the same thermal efficiency. Find Tm in °C.

TH = 700 °CTL = 15 °C
Tm = °C
6.Hard
TH​ = 400 °CTL​ = 30 °CEQH​ = 3200 kJQL​ = 2144 kJW = 1056 kJ

A heat engine takes in 3200 kJ of heat from a reservoir at 400 °C, produces 1056 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 400 °CTL = 30 °CQH = 3200 kJW = 1056 kJ
Sgen = kJ/K

Answer key

  1. 1. Ẇ = 1.25 kW
  2. 2. Q̇L = 10.29 kW
  3. 3. ηmax = 71.13 %
  4. 4. Q̇H = 2.77 kW
  5. 5. Tm = 256.4 °C
  6. 6. Sgen = 2.319 kJ/K

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