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Carnot Cycle

A Carnot's en...

Question

A Carnot's engine takes in a thousand kilo calories of heat from a reservoir at $627^{o} C$ and exhausts it to a sink at $27^{o} C$ .What is its efficiency ?

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Solution

Efficiency is given by the relation:

$η = \frac{W}{Q_{1}} = \frac{Q_{1} - Q_{2}}{Q_{1}} = \frac{T_{1} - T_{2}}{T_{1}}$
$Q_{1} = 1000 K c a l = 10^{6} c a l$
$\Rightarrow T_{1} = 627 + 273 = 900 K$ and $T_{2} = 27 + 273 = 300 K$
$\Rightarrow η = \frac{900 - 300}{900} = 0.667 = 66.67 %$

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