First slide

Heat engine

Question

A Carnot engine whose low temperature reservoir is at $7^{o}$ C has an efficiency of 50%. It is desired to increase the efficiency to 70%.. By how many degrees should the temperature of the high temperature reservoir be increased

Moderate

A

840 K
B

280 K
C

560 K
D

380 K

Solution

Initially $η = \frac{T_{1} - T_{2}}{T_{1}} \Rightarrow 0.5 = \frac{T_{1} - (273 + 7)}{T_{1}}$
$⇒ \frac{1}{2} = \frac{T_{1} - 280}{T_{1}} \Rightarrow T_{1} = 560 K$
Finallly
${η_{1}}^{'} = \frac{{T_{1}}^{'} - T_{2}}{{T_{1}}^{'}} \Rightarrow 0.7 = \frac{{T_{1}}^{'} - (273 + 7)}{{T_{1}}^{'}}$
$\Rightarrow {T_{1}}^{'} = 933 K$
$∴ Increase in temperature$
= 933 - 560 = 373 K $≃$ 380 K

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