Question

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

Answer 1

Answer: (A)

First case : $\eta=1-\frac{100}{300}=\frac{2}{3}$
Second case : $\eta_{\text {net }}=\eta_1+\eta_2-\eta_1 \eta_2$
$\eta_1=1-\frac{200}{300}=\frac{1}{3}$
$ \eta_2=1-\frac{100}{200}=\frac{1}{2}$
$\eta_{\text {net }}=\frac{1}{3}+\frac{1}{2}-\frac{1}{6}=\frac{2}{3}$
$\eta$ (first case) $=\eta$ (second case)