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​ = 4400 kJQL​ = 2860 kJW

A heat engine takes in 4400 kJ of heat from a hot reservoir and rejects 2860 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4400 kJQL = 2860 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 3900 kJQL​ = 2730 kJW = ?

A heat engine takes in 3900 kJ of heat from a hot reservoir and rejects 2730 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3900 kJQL = 2730 kJ
W = kJ
3.Medium
TH​ = 325 °CTL​ = 5 °CEQH​QL​W

A heat engine works between a hot reservoir at 325 °C and a cold reservoir at 5 °C. Find the highest possible thermal efficiency ηmax.

TH = 325 °CTL = 5 °C
ηmax = %
4.Medium
TH​ = 700 °CTL​ = ?EQH​ = 2000 kJQL​ = 602 kJW

A reversible (Carnot) heat engine takes in 2000 kJ of heat from a reservoir at 700 °C and rejects 602 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 700 °CQH = 2000 kJQL = 602 kJ
TL = °C
5.Hard
TH​ = 22 °CTL​ = -10 °CHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump keeps a house at 22 °C while it is -10 °C outside, delivering 11 kW of heat to the house. Find the minimum power input Ẇmin.

TH = 22 °CTL = -10 °CQ̇H = 11 kW
Ẇmin = kW
6.Hard
TH​ = 300 °CTL​ = 10 °CEQH​ = 500 kJQL​ = 300 kJW = 200 kJ

A heat engine takes in 500 kJ of heat from a reservoir at 300 °C, produces 200 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 300 °CTL = 10 °CQH = 500 kJW = 200 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 35 %
  2. 2. W = 1170 kJ
  3. 3. ηmax = 53.5 %
  4. 4. TL = 19.77 °C
  5. 5. Ẇmin = 1.193 kW
  6. 6. Sgen = 0.1871 kJ/K

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