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​ = 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
2.Easy
furnacecooling waterEQ̇H​Q̇L​ = ?Ẇ = 150 MW

A power plant delivers a net power output of 150 MW with a thermal efficiency of 40%. Find the rate Q̇L at which heat is rejected to the cooling water.

Ẇ = 150 MWη = 40%
Q̇L = MW
3.Medium
TH​ = 600 °CTL​ = 10 °CEQH​QL​η = 37%

A heat engine receives heat from a source at 600 °C and rejects heat to the surroundings at 10 °C. Its actual thermal efficiency is 37%. Find its second-law efficiency ηII, the ratio of the actual efficiency to the Carnot efficiency.

TH = 600 °CTL = 10 °Cη = 37%
ηII = %
4.Medium
TH​ = 400 °CTL​ = ?EQH​ = 1500 kJQL​ = 698 kJW

A reversible (Carnot) heat engine takes in 1500 kJ of heat from a reservoir at 400 °C and rejects 698 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 400 °CQH = 1500 kJQL = 698 kJ
TL = °C
5.Hard
950 °CTm​ = ?10 °CABWA​WB​

Two Carnot engines work in series. Engine A receives heat from a reservoir at 950 °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 have the same thermal efficiency. Find Tm in °C.

TH = 950 °CTL = 10 °C
Tm = °C
6.Hard
TH​ = 550 °CTL​ = 40 °CEQH​ = 1400 kJQL​ = 798 kJW = 602 kJ

A heat engine takes in 1400 kJ of heat from a reservoir at 550 °C, produces 602 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 550 °CTL = 40 °CQH = 1400 kJW = 602 kJ
Sgen = kJ/K

Answer key

  1. 1. W = 780 kJ
  2. 2. Q̇L = 225 MW
  3. 3. ηII = 54.76 %
  4. 4. TL = 40.09 °C
  5. 5. Tm = 315.4 °C
  6. 6. Sgen = 0.8475 kJ/K

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