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. $166.7 \,K$
• B. $255.1 \,K$
• C. $266.7\, K$
• D. $367.7 \,K$

Answer 1

Answer: (C)

$266.7\, K$

Answer 2

The correct answer is (C) : $266.7\, K$
Efficiency , $η=1-\frac{T_L}{T_H}$
Given : η = 50%
$\therefore\frac{1}{2}=1-\frac{T_L}{T_H}$
when η increases by 30% then,
$\frac{1}{2}(1.3)=1-(\frac{T_L-40}{T_H})$
$⇒\frac{1}{2}(1.3)=\frac{1}{2}+\frac{40}{T_H}$
$\therefore T_H=266.7\ K$