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:

  1. (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, $\frac{300}{T_1}=1-0.5=0.5$

$\Rightarrow T_1=\frac{300}{0.5}=600 K$

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