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 :

(A) same as the $1^{\text {st }}$ case

(B) always greater than the $1^{\text {st }}$ case

(C) always less than the $1^{\text {st }}$ case

(D) may increase or decrease with respect to the $1^{\text {st }}$ case

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Heat & Thermodynamics

1^{st}

case, Carnot engine operates between temperatures 300 K and 100 K . In

2^{nd}

case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in

2^{nd}

case) will be :

Answer: (A)

First case:

η_{1} = 1 - \frac{100}{300} = \frac{2}{3}

. Second case with two engines in series (300K→200K→100K):

η_{A} = 1 - \frac{200}{300} = \frac{1}{3}

η_{B} = 1 - \frac{100}{200} = \frac{1}{2}

. Combined efficiency:

η_{n e t} = η_{A} + η_{B} - η_{A} η_{B} = \frac{1}{3} + \frac{1}{2} - \frac{1}{6} = \frac{2}{3}

. Thus, both cases have the same efficiency.

JEE Main · 2022 · 27 Jul 2022 · Shift 2 · Single correct option