First slide

Heat engine

Question

A Carnot engine has the same efficiency between 800 K to 500 K and x K to 600 K. The value of x is

Moderate

A

1000 K
B

960 K
C

846 K
D

754 K

Solution

In first case, $(η_{1}) = 1 - \frac{500}{800} = \frac{3}{8}$ and
$is second case, (η_{2}) = 1 - \frac{600}{x}$
Since $η_{1} = η_{2}, therefore \frac{3}{8} = 1 - \frac{600}{x}$
or $\frac{600}{x} = 1 - \frac{3}{8} = \frac{5}{8} or x = \frac{600 \times 8}{5} = 960 K$

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