The slopes of the isothermal and adiabatic $p-V$ graphs of a gas are by $S_I$ and $S_A$ respectively. If the…
The slopes of the isothermal and adiabatic $p-V$ graphs of a gas are by $S_I$ and $S_A$ respectively. If the heat capacity ratio of the gas is $\frac{3}{2}$, then $\frac{S_I}{S_A}=$
$\frac{3}{2}$
$\frac{2}{3}$
$\frac{1}{2}$
$\frac{1}{3}$
Solution
The slope of isothermal $\left(S_I\right)$ and adiabatic $\left(S_A\right)$
$p-V$ graph of gas are related as
Slope of adiabatic $=\gamma \times$ slope of isothermal
$\Rightarrow \quad S_A=\gamma \times S_I \Rightarrow S_I / S_A=1 / \gamma$
$=\frac{1}{3 / 2}$ $\left(\therefore\right.$ Given $\left.\gamma=\frac{3}{2}\right)$
$=2 / 3$