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Question: Gas at a pressure \(P_{0}\) in contained is a vessel. If the masses of all the molecules are halved ...

Gas at a pressure P0P_{0} in contained is 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

4P04P_{0}

B

2P02P_{0}

C

P0P_{0}

D

P02\frac{P_{0}}{2}

Answer

2P02P_{0}

Explanation

Solution

vrms=3Pρ=3PVmv_{rms} = \sqrt{\frac{3P}{\rho}} = \sqrt{\frac{3PV}{m}} ̃ vrms∝Pmv_{rms} \propto \sqrt{\frac{P}{m}}

̃ v1v2=P1P2×m2m1\frac{v_{1}}{v_{2}} = \sqrt{\frac{P_{1}}{P_{2}} \times \frac{m_{2}}{m_{1}}}̃v2v=P0P2×m/2m\frac{v}{2v} = \sqrt{\frac{P_{0}}{P_{2}} \times \frac{m/2}{m}}̃ P2=2P0P_{2} = 2P_{0}