MechanicalThermodynamicseasyFE ExamCoursework

Maximum Efficiency of a Heat Engine

A heat engine operates between a hot reservoir at $T_H = 800\ \text{K}$ and a cold reservoir at $T_C = 300\ \text{K}$ .

Find the maximum possible thermal efficiency of the engine.

Given

T_H	800 K	Hot reservoir temperature
T_C	300 K	Cold reservoir temperature

Hint 1

The maximum efficiency between two reservoirs depends only on their temperatures.

Hint 2

η = 1 − T_C/T_H, with temperatures absolute.

Hint 3

Both values are already in kelvin.

Worked solution — try the problem first

The maximum efficiency of any engine operating between two reservoirs is the Carnot efficiency:

$\eta_{max} = 1 - \frac{T_C}{T_H}$

Both temperatures must be absolute. They already are here, in kelvin — no conversion needed. Using °C would be a serious error.

$\eta_{max} = 1 - \frac{300}{800} = 1 - 0.375 = 0.625$

$\boxed{\eta_{max} = 62.5\%}$

No real engine between these reservoirs can beat this, regardless of working fluid or cycle design. A claim above 62.5% would violate the second law.

Concepts:Carnot cycleSecond law of thermodynamicsThermal efficiency

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