Question

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:

Fig.

• A. Same as the 1st case
• B. Always greater than the 1st case
• C. Always less than the 1st case
• D. May increase or decrease with respect to the 1st case

Answer 1

Answer: (C)

Always less than the 1st case

Answer 2

The correct answer is (C) : Always less than the 1st case
$η_{net} = \frac{W_1+W_2}{Q_1}$
$η_{net} = \frac{W_1}{Q_1}+\frac{W_2}{Q_1}$
$η_{net} = η_1+\frac{W_2}{Q_2}×\frac{Q_2}{Q_1}$
$η_{net} = η_1+(η_2)(1-η_1)$
$1-η_1<1$
$⇒ η_{ne}t<η_1+η_2$