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​ = 3.68 kWẆ = 1.6 kW

A refrigerator removes heat from its cold space at a rate of 3.68 kW while its compressor uses 1.6 kW of power. Find the rate Q̇H at which it rejects heat to the kitchen.

Q̇L = 3.68 kWẆ = 1.6 kW
Q̇H = kW
2.Easy
hot reservoircold reservoirEQH​ = 2600 kJQL​ = 1820 kJW = ?

A heat engine takes in 2600 kJ of heat from a hot reservoir and rejects 1820 kJ to a cold reservoir in each cycle. Find the net work W it produces per cycle.

QH = 2600 kJQL = 1820 kJ
W = kJ
3.Medium
TH​ = 225 °CTL​ = ?EQH​ = 1500 kJQL​ = 943 kJW

A reversible (Carnot) heat engine takes in 1500 kJ of heat from a reservoir at 225 °C and rejects 943 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 225 °CQH = 1500 kJQL = 943 kJ
TL = °C
4.Medium
TH​ = 400 °CTL​ = ?EQH​ = 3100 kJQL​ = 1419 kJW

A reversible (Carnot) heat engine takes in 3100 kJ of heat from a reservoir at 400 °C and rejects 1419 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 400 °CQH = 3100 kJQL = 1419 kJ
TL = °C
5.Hard
700 °CTm​ = ?10 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 700 °C and rejects heat to an intermediate reservoir at temperature Tm. Engine B takes all that heat and rejects heat to a reservoir at 10 °C. Both engines produce the same work. Find Tm in °C.

TH = 700 °CTL = 10 °C
Tm = °C
6.Hard
TH​ = 35 °CTL​ = -25 °CRQ̇H​Q̇L​ = 2.5 kWẆ

A refrigerator keeps its cold space at -25 °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 = -25 °CQ̇L = 2.5 kW
COPmax =

Answer key

  1. 1. Q̇H = 5.28 kW
  2. 2. W = 780 kJ
  3. 3. TL = 40.02 °C
  4. 4. TL = 34.98 °C
  5. 5. Tm = 355 °C
  6. 6. COPmax = 4.136

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