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​ = 3100 kJQL​ = 1705 kJW = ?

A heat engine takes in 3100 kJ of heat from a hot reservoir and rejects 1705 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3100 kJQL = 1705 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 11 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 4.7 delivers 11 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 4.7Q̇H = 11 kW
Ẇ = kW
3.Medium
TH​ = 350 °CTL​ = 40 °CEQH​QL​W

A heat engine works between a hot reservoir at 350 °C and a cold reservoir at 40 °C. Find the highest possible thermal efficiency ηmax.

TH = 350 °CTL = 40 °C
ηmax = %
4.Medium
TH​ = 275 °CTL​ = ?EQH​ = 3500 kJQL​ = 1936 kJW

A reversible (Carnot) heat engine takes in 3500 kJ of heat from a reservoir at 275 °C and rejects 1936 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 275 °CQH = 3500 kJQL = 1936 kJ
TL = °C
5.Hard
TH​ = 600 °CT0​ = 27 °CTL​ = -20 °CERWQ̇H​ = 130 kWQ̇L​ = ?

A Carnot heat engine receives 130 kW of heat from a source at 600 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -20 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 600 °CT0 = 27 °CTL = -20 °CQ̇H = 130 kW
Q̇L = kW
6.Hard
TH​ = 650 °CTL​ = 10 °CEQH​ = 500 kJQL​ = 290 kJW = 210 kJ

A heat engine takes in 500 kJ of heat from a reservoir at 650 °C, produces 210 kJ of work and rejects the rest to a reservoir at 10 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 650 °CTL = 10 °CQH = 500 kJW = 210 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 1395 kJ
  2. 2. Ẇ = 2.34 kW
  3. 3. ηmax = 49.75 %
  4. 4. TL = 30.06 °C
  5. 5. Q̇L = 459.5 kW
  6. 6. Sgen = 0.4826 kJ/K

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