How many times a diatomic gas should be expanded adiabatically so as to reduce the RMS speed to half — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

RMS speed is proportional to $\sqrt{T}$. To halve RMS speed, $T$ must become $1/4$ of its initial value. Using $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$ with $\gamma = 7/5$, we have $T_1 V_1^{2/5} = (T_1/4) V_2^{2/5} \implies (V_2/V_1)^{2/5} = 4 \implies V_2/V_1 = 4^{5/2} = 32$.