Question

Efficiency of a Carnot engine is $26.81\%$ . To increase its efficiency by $20\%$ , its sink temperature will have to be ____. The hot reservoir is maintained at $100^\circ C$ .

• A. increased by $20K$
• B. decreased by $30K$
• C. increased by $30K$
• D. decreased by $20K$

Answer 1

Answer: (D)

Efficiency of the heat engine is,
$\eta=\left(1 - \frac{T_{c o l d}}{T_{h o t}}\right)$
First case :
Let $T_{2 i}$ be the temperature of cold reservoir in the first case.
$\frac{26 . 812}{100}=\left(1 - \frac{T_{2 i}}{373}\right)$
$\Rightarrow T_{2 i}=\frac{73 . 19 \times 373}{100}=273K$
Second case:
Final efficiency $=\frac{20}{100}\times 26.81+26.81$
$=32.172$
Let $T_{2 f}$ be the temperature of sink in the second case,
$\frac{32 . 172}{100}=1-\frac{T_{2 f}}{T_{1}}$
$\frac{T_{2 f}}{373}=1-\frac{32 . 172}{100}$
$T_{2 f}=373\left(1 - \frac{32 . 172}{100}\right)$
$T_{2 f}=253K$
$T_{2 i}-T_{2 f}=20K$