A Carnot engine whose low temperature reservoir is at 7^ C has an… - Vidyadip

MCQ

A Carnot engine whose low temperature reservoir is at $7^{\circ} \mathrm{C}$ has an efficiency of $50 \%$. It is desired to increase the efficiency to $70 \%$. By how many degrees should the temperature of the high temperature reservoir be increased

A
$840 K$
B
$280 K$
C
$560 \mathrm{~K}$
✓
$380 \mathrm{~K}$

✓

Answer

Correct option: D.

$380 \mathrm{~K}$

(d)Initially $ \eta=\frac{T_1-T_2}{T_1} \Rightarrow 0.5=\frac{T_1-(273+7)}{T_1} $
$\Rightarrow \quad \frac{1}{2}=\frac{T_1-280}{T_1}\Rightarrow T_1=560\mathrm{~K}$
Finally $\eta_1{ }^{\prime}=\frac{T_1{ }^{\prime}-T_2}{T_1^{\prime}}\Rightarrow 0.7=\frac{T_1^{\prime}-(273+7)}{T_1^{\prime}} \Rightarrow T_1^{\prime}=933 \mathrm{~K}$
$\therefore$ increase in temperature $=933-560=373 \mathrm{~K} \approx 380 \mathrm{~K}$

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