Question

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

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

Answer 1

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

Given $P\propto T^3$

In adiabatic process,
$P\propto T^{\frac{\gamma }{\gamma -1}}$

i.e., $\frac{\gamma }{\gamma -1}=3$

Solving this equation we get, $\gamma =\frac{3}{2}$