Gas at a pressure `P_(0)` in contained as a vessel. If the masses of all the molecules are halved and their speeds are doubles. The resulting pressure P will be equal to

Options

A. `4P_0`
B. `2P_0`
C. `P_0`
D. `P_0/2`

Answer

B

Explanation

`v_(rms) = sqrt((3P)/rho) = sqrt((3PV)/(m))`
`rArr v_(rms) prop sqrt(P/m)`
Hence,` v_1/v_2 = sqrt(P_1m_2)/(P_2m_1) rArr v/(2v) = sqrt(P_0/P_2 xx (m//2)/m)`
`rArr P_2 = 2P_0`