First slide

Heat engine

Question

The ratio $\frac{W}{Q}$ for a Carnot engine is $\frac{1}{6}$ Now the temperature of o6 sink is reduced by 62^oC, then this ratio becomes twice. The initial temperature of the sink and source are respectively :

Difficult

A

$33^{o} C, 67^{o} C$
B

$37^{o} C, 99^{o} C$
C

$67^{o} C, 33^{o} C$
D

$97 K, 37 K$

Solution

$\frac{W}{Q} = \frac{1}{6} \Rightarrow 1 - \frac{T_{L}}{T_{H}} = \frac{1}{6} \Rightarrow \frac{T_{L}}{T_{H}} = \frac{5}{6}$
If sink temperature decrease by 62^oC then
$1 - \frac{T_{L} - 62}{T_{H}} = 2 \times (\frac{1}{6}) \Rightarrow 2 T_{H} = 3 T_{L} - 186 Hence, T_{H} = 372 K = 99^{o} C and T_{L} = 310 K = 37^{o} C$

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