First slide

Heat engine

Question

A Carnot's engine operates with an efficiency of40% with its sink at $27^{0} C$ . By what amount should the temperature of the source be increased with an aim to increase the efficiency by 10%?

Moderate

A

50 K
B

150 K
C

80 K
D

100 K

Solution

Let $T_{1}$ be the initial temperature of the source, then, using $η = 1 - \frac{T_{2}}{T_{1}}$
We have, $\frac{40}{100} = 1 - \frac{(273 + 27 K)}{T_{1}}$
or $T_{1} = 500 K$
For the efficiency to be 10% more i.e., 50%, let $T_{1}$ ' be the new temperature of the sink,
then, $\frac{50}{100} = 1 - \frac{(273 + 27 K)}{{T^{'}}_{1}}$
or ${T^{'}}_{1} = 600 K$
The required increase in the temperature of the source ${T^{'}}_{1} - T = 600 K - 500 K = 100 K$

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