Question

During an adiabatic process, the pressure of a gas is found to be proportional to the cube of the absolute temperature. The ratio $\frac{C_P}{C_V}=$ for the gas is

• A. 2
• B. 3/2
• C. 5/3
• D. 4/3

Answer 1

The correct option is B 3/2

In an adiabatic process $P{V}^{\gamma }$= constant
Put $V=\frac{RT}{p}$
$\frac{p{R}^{\gamma }{T}^{\gamma }}{P^{\gamma }}$ = constant
Therefore $P^{1-\gamma }{T}^{\gamma }$ = constant
$p\propto T^{\frac{\gamma }{\gamma -1}}$
therefore $\frac{\gamma }{\gamma -1}=3$
$3\gamma -3=\gamma$
$2\gamma =3$
$\gamma =\frac{3}{2}$