Question

A Carnot engine has efficiency of $50\%$. If the temperature of sink is reduced by ${40}^{\circ }C$, its efficiency increases by $30\%$. The temperature of the source will be:

• A. $366.7K$
• B. $255.1K$
• C. $266.7K$
• D. $166.7K$

Answer 1

The correct option is C $266.7K$

Initial efficiency of Carnot engine:
$1-\frac{T_L}{T_H}=0.5\dots \left(1\right)$

Final efficiency of Carnot engine:
$1-\frac{T_L-40}{T_H}=0.65\dots \left(2\right)$
From $\left(1\right)$ and $\left(2\right)$

$\Rightarrow T_H=\frac{800}{3}K\simeq 266.7K$