Thermodynamics Ques 49
49. An ideal carnot engine, whose efficiency is $40 \%$ receives heat at $500 $ $K$. If its efficiency is $50 \%$, then the intake temperature for the same exhaust temperature is
[1995]
(a) $600 $ $K$
(b) $700 $ $K$
(c) $800 $ $K$
(d) $900 $ $K$
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Answer:
Correct Answer: 49.(a)
Solution:
- (a) Efficiency of carnot engine $(\eta_1)=40 \%$ $=0.4$; Initial intake temperature $(T_1)=500$ $ K$ and new efficiency $(\eta_2)=50 \%=0.5$.
Efficiency $(\eta)=1-\frac{T_2}{T_1}$ or $\frac{T_2}{T_1}=1-\eta$.
Therefore in first case, $\frac{T_2}{500}=1-0.4=0.6$.
$\Rightarrow T_2=0.6 \times 500=300$ $ K$
And in second case, $\frac{300}{T_1}=1-0.5=0.5$
$\Rightarrow T_1=\frac{300}{0.5}=600 $ $K$
BETA
