Question

$P-V$ graph for an ideal gas undergoing polytropic process $P V^{m}=$ constant is shown here. Find the value of $m$.

• A. $\frac{3}{4}$
• B. $-\frac{3}{2}$
• C. $\frac{5}{3}$
• D. $\frac{3}{2}$

Answer 1

Answer: (D)

$P V^{m}=$ const.
$\Rightarrow V^{m} d P+m v^{m-1} P d v=0$
$\Rightarrow \frac{d P}{d V}=\frac{-m P}{V}=\tan \left(180-37^{\circ}\right)$
$\Rightarrow \frac{3}{4}=m \frac{2 \times 10^{5}}{4 \times 10^{5}}$
$\Rightarrow m=\frac{3}{2}$