Question

A gas is filled in a rigid container at pressure $P_c$. If the mass of each molecule is halved keeping the total number of molecules same and their r.m.s speed is doubled then find the new pressure.

Answer 1

Relation between pressure of gas, $P$ mass of each molecule $m,$ no. of molecules $N,$ $rms$ speed $\overline{C}:$

$\Rightarrow P_c=\frac{1}{3}\frac{Nm}{V}{\overline{C}}^2$

$\Rightarrow$ Given $m\to \frac{m}{2};$ $\overline{C}\to 2\overline{C}$ then $P$ would be $P=\frac{1}{3}\frac{Nm}{2V}{\overline{C}}^2$

$\Rightarrow P=2\left(\frac{1}{3}\frac{Nm}{V}{\overline{C}}^2\right)$

$\Rightarrow P=2P_c.$

Hence, the answer is $P=2P_c.$