A Carnot engine works first between $200^{\circ} C$ and $0^{\circ} C$ and then between $0^{\circ} C$ and $-200^{\circ} C$. The ratio of its efficiency in the two cases is
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Case 1 :
$T _1=0^{\circ} C =(0+273) K =273 K$
$T _2=200^{\circ}=(200+273) K =473 K$
$\eta_1=1-\frac{ T _1}{ T _2}=1-\frac{273}{473}=0.422$
Case 2:
$T_1=-200^{\circ} C =(-200+273) K =73 K$
$T _2=0^{\circ}=(0+273) K =273 K$
$\eta_2=1-\frac{T_1}{T_2}=1-\frac{73}{273}=0.73$
Ratio of efficiencies, $\eta_1: \eta_2=0.42: 0.73=1: 1.73$
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