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Q. A Carnot's engine is made to work between $200^\circ \,C$ and $0^\circ \,C$ first and then between $0^\circ \,C$ and $-200^\circ \,C$. The ratio of efficiencies of the engine is the two cases is

KCETKCET 2002Thermodynamics

Solution:

$\eta=1-\frac{T_2}{T_1}$
$\therefore \,\eta_1=1-\frac{273}{473}=\frac{200}{473}$
$\eta_1=1-\frac{73}{273}=\frac{200}{273}$
$\therefore \,\eta_1/\eta_2=\frac{273}{473}=\frac{1}{1.73}$