Question

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

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

Answer 1

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

$P\propto T^3$ (given)....(1)
$P{T}^{\frac{\gamma }{1-\gamma }}=K$ ....(2)
By(1) and (2)
$\frac{-\gamma }{1-\gamma }=33-3\gamma =-\gamma 3=2\gamma \gamma =\frac{3}{2}$