A Carnot engine takes $3 \times {10^6}\,cal$. of heat from a reservoir at $627°C$, and gives it to a sink at $27°C.$ The work done by the engine is
AIEEE 2003, Medium
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(b) $\eta = 1 - \frac{{{T_2}}}{{{T_1}}} = \frac{W}{Q}$
==>$W = \left( {1 - \frac{{{T_1}}}{{{T_2}}}} \right)\;Q = \left\{ {1 - \frac{{(273 + 27)}}{{(273 + 627)}}} \right\}$
==>$W = \left( {1 - \frac{{300}}{{900}}} \right) \times 3 \times {10^6}$
$ = 2 \times {10^6} \times 4.2\;J = 8.4 \times {10^6}J$
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