Question

A gas is compressed from some initial volume $V_1$ to final volume $V_f$ along two different paths as shown in figure.

If $W_1,W_2$ corresponds to work done during polytropic process of exponents $n_1,n_2$ respectively, then which of the following statements is/are correct ?

• A. $W_1>W_2$
• B. $n_1>n_2$
• C. $W_1<W_2$
• D. $n_1<n_2$

Answer 1

Answer: (A), (B)

The correct options are
A $W_1>W_2$
B $n_1>n_2$

From the figure, we can deduce that, Area under process $P{V}^{n_1}=$ constant is greater than the area under process $P{V}^{n_2}=$ constant
Thus, $W_1>W_2$
and,
Slope of $1>$ Slope of $2$
$\therefore n_1>n_2$
Thus, options (a) and (b) are correct.