A carnot engine rejects 80 mj of energy every hour by transferring heat to areservoir at 10°c. determine the temperature of the high-temperature reservoir and the power produced if the rate of energy addition is 40 kw.

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02-08-2017
Physics

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A carnot engine rejects 80 mj of energy every hour by transferring heat to areservoir at 10°c. determine the temperature of the high-temperature reservoir and the power produced if the rate of energy addition is 40 kw.

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Erythrosin17 Erythrosin17 · Answer 1 · 2017-08-15T01:08:56+02:00

The Carnot engine is a heat engine that operates based on the reversible Carnot cycle. It is perceived as the ideal heat engine. To determine the temperature and the power that is produced by the Carnot engine, we make use of the definition of its efficiency.

Efficiency = net work / heat in
where net work = heat in - heat out
Efficiency = heat in - heat out / heat in
= 1 - heat out / heat in = 1 - Tl / Th

where Tl is the temperature that is colder and Th is the hotter temperature.

heat out = 80 MJ / hr ( 1x10^6 J / 1 MJ ) ( 1 hr / 3600 s ) ( 1 KJ / 1000 J )= 22.22 KJ / s = 22.22 kW = power produced
heat in = 40 kW

Efficiency = 1 - heat out / heat in = 1 - (22.22 / 40) = 0.4445
0.4445 = 1 - (10+273.15) / Th
Th = 509.72 K = 236.57 degrees Celsius