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 2.7 delivers 10.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 2.7Q̇H = 10.5 kW
Ẇ = kW
2.Easy
hot reservoircold reservoirEQH​ = 2800 kJQL​ = 2240 kJW = ?

A heat engine takes in 2800 kJ of heat from a hot reservoir and rejects 2240 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2800 kJQL = 2240 kJ
W = kJ
3.Medium
TH​ = 200 °CTL​ = 25 °CEQH​ = 3200 kJQL​W = ?

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 25 °C. It takes in 3200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 200 °CTL = 25 °CQH = 3200 kJ
Wmax = kJ
4.Medium
TH​ = 400 °CTL​ = 40 °CEQH​ = 2200 kJQL​W = ?

A heat engine works between a hot reservoir at 400 °C and a cold reservoir at 40 °C. It takes in 2200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 400 °CTL = 40 °CQH = 2200 kJ
Wmax = kJ
5.Hard
TH​ = 21 °CTL​ = -10 °CHPQ̇H​ = 5 kWQ̇L​Ẇ

A heat pump keeps a house at 21 °C while it is -10 °C outside, delivering 5 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 21 °CTL = -10 °CQ̇H = 5 kW
COPmax =
6.Hard
TH​ = 30 °CTL​ = -18 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 30 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 30 °CTL = -18 °CQ̇L = 1.5 kW
Ẇmin = kW

Answer key

  1. 1. Ẇ = 3.889 kW
  2. 2. W = 560 kJ
  3. 3. Wmax = 1184 kJ
  4. 4. Wmax = 1177 kJ
  5. 5. COPmax = 9.489
  6. 6. Ẇmin = 0.2822 kW

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