Q68 / 90 · JEE Main 2022 (27 Jul Shift 2) · Physics

In $1^{st}$ 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 :

Correct answer
A
same as the $1^{st}$ case
B
always greater than the $1^{st}$ case
C
always less than the $1^{st}$ case
D
may increase or decrease with respect to the $1^{st}$ case

Solution

The efficiency of a Carnot engine operating between two temperatures is given by $η = 1 - \frac{T_{L}}{T_{H}}$
For the first case : $η = 1 - \frac{100}{300} = \frac{2}{3}$
For the second case : $η_{net} = η_{1} + η_{2} - η_{1} η_{2}$
$η_{1} = 1 - \frac{200}{300} = \frac{1}{3}$
$η_{2} = 1 - \frac{100}{200} = \frac{1}{2}$
$η_{net} = \frac{1}{3} + \frac{1}{2} - \frac{1}{6} = \frac{2}{3}$
$η$ (first case) $= η$ (second case)

Hence, the correct answer is option: 'A'.

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In 1st case, Carnot engine operates between temperatures 300 K and 100 K. In 2nd case, as shown in the figure, a combination of two engines is used. The efficiency of this combination (in 2nd case) will be :

Solution

Relevant Questions

In $1^{st}$ 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 :