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

Options

A. `900 K`
B. `600 K`
C. `400 K`
D. `700 K`

Answer

B

Explanation

Let `T_2` be the exhaust temperature.
In the first case, `T_1 = 500 K, eta = 40 % = 0A" "eta = (T_1 - T_2)/T_1 rArr 0.4 = (500 - T_2)/500 rArr T_2 = 300 K`
Now, in second case, `T_2 = 300 K, eta = 50 % = 0.5, " "eta = (T_1 - T_2)/T_1 rArr 0.5 =(T_1 - 300)/T_1 rArr T_1 = 600 K`