Thermodynamics - Result Question 50
53. 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: 53. (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, $\frac{300}{T_1}=1-0.5=0.5$
$\Rightarrow T_1=\frac{300}{0.5}=600 K$
