Question

During an adiabatic process, the pressure of a gas is proportional to the cube of its adiabatic temperature. The value of $\frac{C_p}{C_v}$ for that gas is :

• A. $\frac{4}{3}$
• B. $2$
• C. $\frac{5}{3}$
• D. $\frac{3}{2}$

Answer 1

The correct option is D $\frac{3}{2}$

Given: $P\alpha T^3\to \left(1\right)$
in adiabatic process relation between P and T is :
$P^{1-\gamma }{T}^{\gamma }=constant$
$P\alpha T^{\frac{\gamma }{\gamma -1}}\to \left(2\right)$
And we know, for a gas $\frac{C_p}{C_v}=\gamma$
From equation 1 and 2:
$\frac{\gamma }{\gamma -1}=3$
So, $\gamma =\frac{3}{2}$
So, $\frac{C_p}{C_v}=\frac{3}{2}$