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​ = 10.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 4.4 delivers 10.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 4.4Q̇H = 10.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 4600 kJQL​ = 3220 kJW

A heat engine takes in 4600 kJ of heat from a hot reservoir and rejects 3220 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4600 kJQL = 3220 kJ
η = %
3.Medium
TH​ = 275 °CTL​ = 35 °CEQH​ = 1100 kJQL​W = ?

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 35 °C. It takes in 1100 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 275 °CTL = 35 °CQH = 1100 kJ
Wmax = kJ
4.Medium
TH​ = 500 °CTL​ = ?EQH​ = 4400 kJQL​ = 1697 kJW

A reversible (Carnot) heat engine takes in 4400 kJ of heat from a reservoir at 500 °C and rejects 1697 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 500 °CQH = 4400 kJQL = 1697 kJ
TL = °C
5.Hard
TH​ = 900 °CTL​ = 15 °CEQH​ = 2000 kJQL​ = 1240 kJW = 760 kJ

A heat engine takes in 2000 kJ of heat from a reservoir at 900 °C, produces 760 kJ of work and rejects the rest to a reservoir at 15 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 900 °CTL = 15 °CQH = 2000 kJW = 760 kJ
Sgen = kJ/K
6.Hard
TH​ = 28 °CTL​ = -10 °CRQ̇H​Q̇L​ = 1 kWẆ = ?

A refrigerator keeps its cold space at -10 °C in a kitchen at 28 °C, removing heat from the cold space at 1 kW. Find the minimum power input Ẇmin.

TH = 28 °CTL = -10 °CQ̇L = 1 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 8.114 kW
  2. 2. η = 30 %
  3. 3. Wmax = 481.6 kJ
  4. 4. TL = 25.04 °C
  5. 5. Sgen = 2.599 kJ/K
  6. 6. Ẇmin = 0.1444 kW

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