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​ = 1900 kJQL​ = 1425 kJW = ?

A heat engine takes in 1900 kJ of heat from a hot reservoir and rejects 1425 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 1900 kJQL = 1425 kJ
W = kJ
2.Easy
houseoutside airHPQ̇H​ = 15 kWQ̇L​Ẇ = ?

A heat pump with a coefficient of performance of 3.6 delivers 15 kW of heat to a house. Find the electrical power Ẇ it uses.

COPHP = 3.6Q̇H = 15 kW
Ẇ = kW
3.Medium
TH​ = 250 °CTL​ = 25 °CEQH​ = 700 kJQL​W = ?

A heat engine works between a hot reservoir at 250 °C and a cold reservoir at 25 °C. It takes in 700 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 250 °CTL = 25 °CQH = 700 kJ
Wmax = kJ
4.Medium
TH​ = 700 °CTL​ = ?EQH​ = 2100 kJQL​ = 676 kJW

A reversible (Carnot) heat engine takes in 2100 kJ of heat from a reservoir at 700 °C and rejects 676 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 700 °CQH = 2100 kJQL = 676 kJ
TL = °C
5.Hard
TH​ = 400 °CT0​ = 27 °CTL​ = -5 °CERWQ̇H​ = 170 kWQ̇L​ = ?

A Carnot heat engine receives 170 kW of heat from a source at 400 °C and rejects heat to the surroundings at 27 °C. All of its work drives a Carnot refrigerator that removes heat from a freezer at -5 °C and also rejects heat to the surroundings at 27 °C. Find the rate Q̇L at which heat is removed from the freezer.

TH = 400 °CT0 = 27 °CTL = -5 °CQ̇H = 170 kW
Q̇L = kW
6.Hard
TH​ = 32 °CTL​ = -10 °CRQ̇H​Q̇L​ = 1.5 kWẆ

A refrigerator keeps its cold space at -10 °C in a kitchen at 32 °C, removing heat from the cold space at 1.5 kW. Find the highest possible coefficient of performance COPmax.

TH = 32 °CTL = -10 °CQ̇L = 1.5 kW
COPmax =

Answer key

  1. 1. W = 475 kJ
  2. 2. Ẇ = 4.167 kW
  3. 3. Wmax = 301.1 kJ
  4. 4. TL = 40.11 °C
  5. 5. Q̇L = 789.4 kW
  6. 6. COPmax = 6.265

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