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​ = 3700 kJQL​ = 2405 kJW = ?

A heat engine takes in 3700 kJ of heat from a hot reservoir and rejects 2405 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 3700 kJQL = 2405 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 17.5 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3 delivers 17.5 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3Q̇H = 17.5 kW
Ẇ = kW
3.Medium
TH​ = 625 °CTL​ = 20 °CEQH​ = 5000 kJQL​W = ?

A heat engine works between a hot reservoir at 625 °C and a cold reservoir at 20 °C. It takes in 5000 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 625 °CTL = 20 °CQH = 5000 kJ
Wmax = kJ
4.Medium
TH​ = 250 °CTL​ = ?EQH​ = 1700 kJQL​ = 1066 kJW

A reversible (Carnot) heat engine takes in 1700 kJ of heat from a reservoir at 250 °C and rejects 1066 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 250 °CQH = 1700 kJQL = 1066 kJ
TL = °C
5.Hard
TH​ = 32 °CTL​ = -25 °CRQ̇H​Q̇L​ = 3 kWẆ

A refrigerator keeps its cold space at -25 °C in a kitchen at 32 °C, removing heat from the cold space at 3 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = -25 °CQ̇L = 3 kW
COPmax =
6.Hard
TH​ = 45 °CTL​ = 10 °CHPQ̇H​ = 15.5 kWQ̇L​Ẇ = ?

A heat pump delivers 15.5 kW of heat to a heating system at 45 °C, taking heat from a source at 10 °C. Its actual COP is 60% of the Carnot COP between these temperatures. Find the electrical power Ẇ it uses.

TH = 45 °CTL = 10 °CηII = 60%Q̇H = 15.5 kW
Ẇ = kW

Answer key

  1. 1. W = 1295 kJ
  2. 2. Ẇ = 5.833 kW
  3. 3. Wmax = 3368 kJ
  4. 4. TL = 54.9 °C
  5. 5. COPmax = 4.354
  6. 6. Ẇ = 2.842 kW

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