Question

A Carnot engine works between ice point and steam point. In order to increase the efficiency of the engine by $20$ %, its sink temperature will have to be

• A. increased by 20 K.
• B. decreased by 20 K.
• C. increased by ${20}^{o}C$.
• D. decreased by ${25}^{o}C$.

Answer 1

Answer: (B)

decreased by 20 K.

Efficiency of a Carnot engine$\left(\eta \right)=1-\frac{T_c}{T_h}$
$=1-\frac{273}{373}=0.268$
i.e 26.8% is the efficiency.

To increase the efficiency of the engine by 20%, i.e. $0.2\times 0.268=0.0536$
New efficiency is $0.268+0.0536=0.3216$

$0.3216=1-\frac{T_c}{373}$
$T_c=0.6784\times 373=253.04K$
$273-253=20K$, sink temperature has to be decreased by 20K
Option B.