Question

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

Answer 1

Answer: 1.50

Slope $=-\frac{\gamma P}{V}=-\tan 37^{\circ }$
$\Rightarrow \frac{mP}{V}=\tan 37^{\circ }$
$\Rightarrow m=\left(\frac{V}{P}\right)\left(\frac{3}{4}\right)$
$=\left(\frac{4\times 10^5}{2\times 10^5}\right)\left(\frac{3}{4}\right)$
$=\frac{3}{2}=1.5$