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
kitchencold spaceRQ̇H​ = ?Q̇L​ = 5.32 kWẆ = 1.9 kW

A refrigerator removes heat from its cold space at a rate of 5.32 kW while its compressor uses 1.9 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 5.32 kWẆ = 1.9 kW
Q̇H = kW
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 200 MW

A power plant delivers a net power output of 200 MW with a thermal efficiency of 35%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 200 MWη = 35%
Q̇H = MW
3.Medium
TH​ = 225 °CTL​ = ?EQH​ = 2900 kJQL​ = 1590 kJW

A reversible (Carnot) heat engine takes in 2900 kJ of heat from a reservoir at 225 °C and rejects 1590 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 225 °CQH = 2900 kJQL = 1590 kJ
TL = °C
4.Medium
TH​ = 200 °CTL​ = 25 °CEQH​ = 4200 kJQL​W = ?

A heat engine works between a hot reservoir at 200 °C and a cold reservoir at 25 °C. It takes in 4200 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 200 °CTL = 25 °CQH = 4200 kJ
Wmax = kJ
5.Hard
TH​ = 550 °CTL​ = 30 °CEQH​ = 3000 kJQL​ = 2040 kJW = 960 kJ

A heat engine takes in 3000 kJ of heat from a reservoir at 550 °C, produces 960 kJ of work and rejects the rest to a reservoir at 30 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 550 °CTL = 30 °CQH = 3000 kJW = 960 kJ
Sgen = kJ/K
6.Hard
TH​ = 28 °CTL​ = 4 °CRQ̇H​Q̇L​ = 4 kWẆ

A refrigerator keeps its cold space at 4 °C in a kitchen at 28 °C, removing heat from the cold space at 4 kW. Find the highest possible coefficient of performance COPmax.

TH = 28 °CTL = 4 °CQ̇L = 4 kW
COPmax =

Answer key

  1. 1. Q̇H = 7.22 kW
  2. 2. Q̇H = 571.4 MW
  3. 3. TL = −0.02638 °C
  4. 4. Wmax = 1553 kJ
  5. 5. Sgen = 3.085 kJ/K
  6. 6. COPmax = 11.55

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