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​ = 14.5 kWQ̇L​ = ?Ẇ

A heat pump with a coefficient of performance of 3.4 delivers 14.5 kW of heat to a house. Find the rate Q̇L at which it takes heat from the outside air.

COPHP = 3.4Q̇H = 14.5 kW
Q̇L = kW
2.Easy
hot reservoircold reservoirEQH​ = 3200 kJQL​ = 2240 kJW = ?

A heat engine takes in 3200 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 = 3200 kJQL = 2240 kJ
W = kJ
3.Medium
TH​ = 750 °CTL​ = ?EQH​ = 3100 kJQL​ = 888 kJW

A reversible (Carnot) heat engine takes in 3100 kJ of heat from a reservoir at 750 °C and rejects 888 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 750 °CQH = 3100 kJQL = 888 kJ
TL = °C
4.Medium
TH​ = 775 °CTL​ = 15 °CEQH​ = 4000 kJQL​W = ?

A heat engine works between a hot reservoir at 775 °C and a cold reservoir at 15 °C. It takes in 4000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 775 °CTL = 15 °CQH = 4000 kJ
Wmax = kJ
5.Hard
TH​ = 35 °CTL​ = -20 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at -20 °C in a kitchen at 35 °C, removing heat from the cold space at 2.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 35 °CTL = -20 °CQ̇L = 2.5 kW
COPmax =
6.Hard
TH​ = 25 °CTL​ = -18 °CRQ̇H​Q̇L​ = 1.5 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 25 °C, removing heat from the cold space at 1.5 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = -18 °CQ̇L = 1.5 kW
Ẇmin = kW

Answer key

  1. 1. Q̇L = 10.24 kW
  2. 2. W = 960 kJ
  3. 3. TL = 19.93 °C
  4. 4. Wmax = 2900 kJ
  5. 5. COPmax = 4.603
  6. 6. Ẇmin = 0.2528 kW

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