Question

Under an adiabatic process, the volume of an ideal gas gets doubled. Consequently the mean collision time between the gas molecule changes from $\tau_{1}$ to $\tau_{2}.$ If $\frac{C_{p}}{C_{v}}=\gamma$
for this gas then a good estimate for $\frac{\tau_{2}}{\tau_{1}}$ is given by :

• A. $\left(\frac{1}{2}\right)^{\frac{\gamma+1}{2}}$
• B. $\frac{1}{2}$
• C. $\left(\frac{1}{2}\right)^{\gamma}$
• D. $2$

Answer 1

Answer: (A)

$t \propto \frac{V}{\sqrt{T}}\quad....\left(1\right)$
$TV^{\gamma-1} =$ constant $\quad....\left(2\right)$
$\therefore t \propto V^{\frac{\gamma+1}{2}}$