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​ = 3600 kJQL​ = 1980 kJW = ?

A heat engine takes in 3600 kJ of heat from a hot reservoir and rejects 1980 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3600 kJQL = 1980 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 7 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.8 delivers 7 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.8Q̇H = 7 kW
Ẇ = kW
3.Medium
TH​ = 550 °CTL​ = 35 °CEQH​QL​W

A heat engine works between a hot reservoir at 550 °C and a cold reservoir at 35 °C. Find the highest possible thermal efficiency ηmax.

TH = 550 °CTL = 35 °C
ηmax = %
4.Medium
TH​ = 400 °CTL​ = 15 °CEQH​ = 3600 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 15 °C. It takes in 3600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 15 °CQH = 3600 kJ
Wmax = kJ
5.Hard
1050 °CTm​ = ?40 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 1050 °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 produce the same work. Find Tm in °C.

TH = 1050 °CTL = 40 °C
Tm = °C
6.Hard
TH​ = 700 °CTL​ = 30 °CEQH​ = 4600 kJQL​ = 2392 kJW = 2208 kJ

A heat engine takes in 4600 kJ of heat from a reservoir at 700 °C, produces 2208 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 700 °CTL = 30 °CQH = 4600 kJW = 2208 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 1620 kJ
  2. 2. Ẇ = 1.842 kW
  3. 3. ηmax = 62.56 %
  4. 4. Wmax = 2059 kJ
  5. 5. Tm = 545 °C
  6. 6. Sgen = 3.164 kJ/K

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