First slide

Heat engine

Question

Efficiency of a Carnot engine is 50% when temperature of outlet is 500 K. ln order to increase efficiency up to 60% keeping temperature of intake the same what is temperature of outlet?

Moderate

A

200 K
B

400 K
C

600 K
D

800 K

Solution

$η = 1 - \frac{T_{2}}{T_{1}} \Rightarrow \frac{1}{2} = 1 - \frac{500}{T_{1}} \Rightarrow \frac{500}{T_{1}} = \frac{1}{2}$ -----(i)
$\frac{60}{100} = 1 - \frac{{T_{2}}^{'}}{T_{1}} \Rightarrow \frac{{T_{2}}^{'}}{T_{1}} = \frac{2}{5} - - - - - - - - - - (ii)$
Dividing equation (i) by (ii), $\frac{500}{{T_{2}}^{'}} = \frac{5}{4} \Rightarrow T_{2} = 400 K$

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