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​ = 4700 kJQL​ = 3290 kJW

A heat engine takes in 4700 kJ of heat from a hot reservoir and rejects 3290 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 4700 kJQL = 3290 kJ
η = %
2.Easy
hot reservoircold reservoirEQH​ = 2000 kJQL​ = 1600 kJW = ?

A heat engine takes in 2000 kJ of heat from a hot reservoir and rejects 1600 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2000 kJQL = 1600 kJ
W = kJ
3.Medium
TH​ = 275 °CTL​ = 10 °CEQH​ = 2900 kJQL​W = ?

A heat engine works between a hot reservoir at 275 °C and a cold reservoir at 10 °C. It takes in 2900 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 275 °CTL = 10 °CQH = 2900 kJ
Wmax = kJ
4.Medium
TH​ = 250 °CTL​ = ?EQH​ = 2500 kJQL​ = 1329 kJW

A reversible (Carnot) heat engine takes in 2500 kJ of heat from a reservoir at 250 °C and rejects 1329 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 250 °CQH = 2500 kJQL = 1329 kJ
TL = °C
5.Hard
TH​ = 20 °CTL​ = -10 °CHPQ̇H​ = 5 kWQ̇L​Ẇ

A heat pump keeps a house at 20 °C while it is -10 °C outside, delivering 5 kW of heat to the house. Find the highest possible coefficient of performance COPmax.

TH = 20 °CTL = -10 °CQ̇H = 5 kW
COPmax =
6.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 3.5 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 3.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = -10 °CQ̇L = 3.5 kW
COPmax =

Answer key

  1. 1. η = 30 %
  2. 2. W = 400 kJ
  3. 3. Wmax = 1402 kJ
  4. 4. TL = 4.957 °C
  5. 5. COPmax = 9.772
  6. 6. COPmax = 6.265

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