A gas at pressure P0 is contained in a vessel. If the masses of all the molecules are halved and their speeds doubled, the resulting pressure would be

Question

A gas at pressure P0 is contained in a vessel. If the masses of all the molecules are halved and their speeds doubled, the resulting pressure would be (A)  4 P0  (B)  2 P0  (C)  P0  (D)  (p0/2)

Tardigrade Admin · Accepted Answer

The pressure p extorted by a perfect gas on the walls of the containing vessel is given by p = (1/3) (mnc2/v) According to the question, P = P0 m = m0 where, n = number of molecules c = speed of molecules According to question, m' = (m0/2) c' = 2c p' = p'0 P'0 = (1/3)((m0/2))× n× (2c)2 = (1/3) m0nc2 ⋅ 2 = p0 × 2 = 2 p0

Q. A gas at pressure $P_{0}$ is contained in a vessel. If the masses of all the molecules are halved and their speeds doubled, the resulting pressure would be

$4 P_{0}$

$2 P_{0}$

$P_{0}$

$\frac{p _{0}}{2}$

Q. A gas at pressure P0​ is contained in a vessel. If the masses of all the molecules are halved and their speeds doubled, the resulting pressure would be

4P0​

2P0​

P0​

2p0​​

Q. A gas at pressure $P_{0}$ is contained in a vessel. If the masses of all the molecules are halved and their speeds doubled, the resulting pressure would be

$4 P_{0}$

$2 P_{0}$

$P_{0}$

$\frac{p _{0}}{2}$