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. 1200 K
• B. 750 K
• C. 600 K
• D. 800 K

Answer 1

The correct option is B 750 K

For carnot engine-

$\eta \left(efficiency\right)=1-\frac{T_L}{T_H}$

$T_L=$ low temperature(sink)

$\frac{40}{100}=1-\frac{T_L}{500}\Rightarrow \frac{T_L}{500}=\frac{60}{100}\Rightarrow T_L=300$

Now,

$\frac{60}{100}=1-\frac{300}{T_H}\frac{300}{T_H}=1-\frac{60}{100}\frac{300}{T_H}=\frac{40}{100}{T}_H=\frac{300\times 100}{40}=750K$