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​ = 3100 kJQL​ = 2480 kJW

A heat engine takes in 3100 kJ of heat from a hot reservoir and rejects 2480 kJ to a cold reservoir in each cycle. Find its thermal efficiency η.

QH = 3100 kJQL = 2480 kJ
η = %
2.Easy
furnacecooling waterEQ̇H​ = ?Q̇L​Ẇ = 100 MW

A power plant delivers a net power output of 100 MW with a thermal efficiency of 55%. Find the rate of heat input Q̇H from the fuel.

Ẇ = 100 MWη = 55%
Q̇H = MW
3.Medium
TH​ = 225 °CTL​ = 25 °CEQH​ = 3600 kJQL​W = ?

A heat engine works between a hot reservoir at 225 °C and a cold reservoir at 25 °C. It takes in 3600 kJ of heat. Find the most work Wmax it could possibly produce.

TH = 225 °CTL = 25 °CQH = 3600 kJ
Wmax = kJ
4.Medium
TH​ = 450 °CTL​ = ?EQH​ = 2900 kJQL​ = 1115 kJW

A reversible (Carnot) heat engine takes in 2900 kJ of heat from a reservoir at 450 °C and rejects 1115 kJ per cycle. Find the temperature TL of the cold reservoir in °C.

TH = 450 °CQH = 2900 kJQL = 1115 kJ
TL = °C
5.Hard
TH​ = 25 °CTL​ = -18 °CRQ̇H​Q̇L​ = 4 kWẆ = ?

A refrigerator keeps its cold space at -18 °C in a kitchen at 25 °C, removing heat from the cold space at 4 kW. Find the minimum power input Ẇmin.

TH = 25 °CTL = -18 °CQ̇L = 4 kW
Ẇmin = kW
6.Hard
TH​ = 900 °CTL​ = 40 °CEQH​ = 3200 kJQL​ = 1792 kJW = 1408 kJ

A heat engine takes in 3200 kJ of heat from a reservoir at 900 °C, produces 1408 kJ of work and rejects the rest to a reservoir at 40 °C, per cycle. Find the total entropy generated Sgen per cycle.

TH = 900 °CTL = 40 °CQH = 3200 kJW = 1408 kJ
Sgen = kJ/K

Answer key

  1. 1. η = 20 %
  2. 2. Q̇H = 181.8 MW
  3. 3. Wmax = 1445 kJ
  4. 4. TL = 4.889 °C
  5. 5. Ẇmin = 0.6741 kW
  6. 6. Sgen = 2.995 kJ/K

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