First slide

Heat engine

Question

A carnot engine has an efficiency of 40%. Keeping the source temperature unchanged, what should be the percentage change in the temperature of the sink in order to increase the efficiency by 10%?

Easy

A

4.44% increase
B

3.64%, decrease
C

6.66% decrease
D

5.18% increase

Solution

$1 - \frac{T_{2}}{T_{1}} = η \Rightarrow T_{2} = T_{1} (1 - η)$
Initially, $T_{2} = T_{1} (1 - 0.4) = 0.6 T_{1}$
Finally, $T_{2}^{1} = T_{1} [1 - (0.4 + \frac{10}{100} \times 0.4)] = 0.56 T_{1}$
$∴ \frac{T_{2} - T_{2}^{1}}{T_{2}} = \frac{0.6 T_{1} - 0.56 T_{1}}{0.6 T} = 6.66 %$
So temperature of the sink should be decreased by 6.66%

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