question_answer

A gas in a closed vessel is at the pressure \[{{P}_{0}}\] . If the masses of all the molecules be made half and their speeds be made double, then find the resultant pressure.

Answer:

                \[{{P}_{0}}=\frac{1}{3}\frac{mN}{V}{{\upsilon }^{2}}\]                 \[\therefore \]  \[P'=\frac{1}{3}\frac{(m/2)}{V}{{(2\upsilon )}^{2}}=\frac{2}{3}\frac{mN}{V}{{\upsilon }^{2}}=\mathbf{2}{{\mathbf{P}}_{\mathbf{0}}}\]