Maximum Efficiency Problem

Question

What would the high temperature need to be if a steam engine were to achieve 50% efficiency? (the heat sink is 100°C.)

Answer 1

The efficiency of the cycle is given as η=1−(T₁​/T₂​)​.

Here T₁​ is the temperature of the source and T₂​ is the temperature of the sink.

The temperature of the sink is given as 100 ^oC, or 373 K

Thus we get 0.5=1−(T₁​/373)​.

We can make T₁ the subject of the formula.

0.5*373=373*1−(T₁​/373)*373​.

(0.5*373)-373=−T₁

-186.5 =​−T₁

T₁ = 186.5K

or

T₁​=186.5K=-85.65^oC