Question

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

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

Answer 1

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

For adiabatic process $\frac{C_P}{C_V}=\gamma$
$P\propto T^3$
$P{T}^{-3}=$ constant ... (1)
for adiabatic process pressure temperature relationship is given by
$P.T^{\frac{\gamma }{1-\gamma }}=$ constant ... (2)
from equation (1) and (2)
$\frac{\gamma }{1-\gamma }=(-3)$
$\Rightarrow \gamma =-3+3\gamma$
$3=3\gamma -\gamma$
$\gamma =\frac{3}{2}=\left(\frac{C_P}{C_V}\right)$