A Carnot's engine is made to work between 200^ C and 0^ C first a… - Vidyadip

MCQ

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

✓
$1.73: 1$
B
$1: 1.73$
C
$1: 1$
D
$1: 2$

✓

Answer

Correct option: A.

$1.73: 1$

In first case $\eta_1=1-\frac{T_2}{T_1}=1-\frac{(273+0)}{(273+200)}=\frac{200}{473}$
In second case $\eta_2=1-\frac{(273-200)}{(273+0)}=\frac{200}{273}$
$\Rightarrow\frac{\eta_1}{\eta_2}=\frac{1}{\left(\frac{473}{273}\right)}=1: 1.73$

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