Q 11-11-110JEE MainJEE Main 2022 (27 Jul, Shift 2)Easy
In $1^{\text{st}}$ case, Carnot engine operates between temperatures $300$ K and $100$ K. In $2^{\text{nd}}$ case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in $2^{\text{nd}}$ case) will be :
Answer: (A) same as the $1^{\text{st}}$ case
Let $E_1$ take $Q_1$ from 300 K. It rejects $Q_2 = Q_1\dfrac{200}{300}$ at 200 K, which $E_2$ takes in, rejecting $Q_3 = Q_2\dfrac{100}{200} = Q_1\dfrac{100}{300}$ at 100 K.
$$\eta = 1 - \frac{Q_3}{Q_1} = 1 - \frac{100}{300} = \frac23$$
This equals the efficiency of a single Carnot engine between 300 K and 100 K.
Solution by Sreeraj P, M.Sc Physics