Question

During on adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature, the ratio of $\frac{C_p}{C_v}$ for the gas is ?

Answer 1

For adiabatic process $C_P/C_V=\gamma$

$P\propto T^3=P{T}^3$= constant

For, adiabatic process $P{T}^{\gamma /1-r}$= constant

From both equation $\frac{\gamma }{1-\gamma }=-3$

$\Rightarrow \gamma =3\gamma -3$

$\Rightarrow \gamma =3/2$

$\therefore C_P/C_V=3/2$