Thermodynamics - Result Question 46

48. A Carnot engine whose efficiency is $50 %$ has an exhaust temperature of $500 K$. If the efficiency is to be $60 %$ with the same intake temperature, the exhaust temperature must be (in $K$ )

[2002]

(a) 800

(b) 200

(c) 400

(d) 600

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Answer:

Correct Answer: 48. (c)

Solution:

$ \begin{aligned} & \text{ (c) } \eta=1-\frac{T_2}{T_1} \text{ or } \frac{50}{100}=1-\frac{500}{T_1} \\ & \Rightarrow T_1=1000 K \end{aligned} $

Also, $\frac{60}{100}=1-\frac{T_2}{1000} \Rightarrow T_2=400 K$