Question

A Carnot engine, whose efficiency is $40\%$, takes in heat from a source maintained at a temperature of $500\, K$. It is desired to have an engine of efficiency $60\%$. Then, the intake temperature for the same exhaust (sink) temperature must be :

• A. efficiency of carnot engine cannot be made larger than $50\%$
• B. $1200\, K$
• C. $750\, K$
• D. $600\, K$

Answer 1

Answer: (C)

For $1^{st}$ case
efficiency $-\eta=\left(1-\frac{T_{1}}{T_{2}}\right)\times100
\left(1-\frac{T_{1}}{500}\right)\times 100=40$
$T_{1}=300\,K$
for $2^{nd}$ case
$\eta=\left(1-\frac{300}{T_{2}}\right)\times 100=60$
$T_{1}=750\,K$