Question

Gas at a pressure $P_{0}$ in contained as a vessel. If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to

• A. $4P_{0}$
• B. $2P_{0}$
• C. $P_{0}$
• D. $\frac{P_{0}}{2}$

Answer 1

Answer: (B)

$2P_{0}$

Answer 2

$P = \frac{1}{3}\frac{mN}{V}v_{rms}^{2}$

∴ $P \propto mv_{rms}^{2}$

so $\frac{P_{2}}{P_{1}} = \frac{m_{2}}{m_{1}} \times \left( \frac{v_{2}}{v_{1}} \right)^{2} = \frac{m_{1} ⥂ / ⥂ 2}{m_{1}}\left( \frac{2v_{1}}{v_{1}} \right)^{2} = 2$

⇒ $P_{2} = 2P_{1} = 2P_{0}$