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