Gas at a pressure P0 is contained in a vessel . If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to

Question

Gas at a pressure P0 is contained in 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) 4P0 (B) 2P0 (C) P0 (D) (P0/2)

Tardigrade Admin · Accepted Answer

P =(1/3) ( mN / V 2) v rms 2 ∴ p propto mv rms 2 so ( P 2/ P 1)=( m 2/ m 2) ×(( v 2/ v 1))2 =( m 1 / 2/ m 1)((2 v 1/ v 1))2 =2 P 2=2 P 1 =2 P 0

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

$4 P_{0}$

$2 P_{0}$

$P_{0}$

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

$P = \frac{1}{3} \frac{m N}{V _{2}} v_{r m s}^{2}$
$∴ p \propto m v_{r m s}^{2}$
$so \frac{P _{2}}{P _{1}} = \frac{m _{2}}{m _{2}} \times (\frac{v _{2}}{v _{1}})^{2}$
$= \frac{m _{1} /2}{m _{1}} (\frac{2 v _{1}}{v _{1}})^{2}$
$= 2$
$P_{2} = 2 P_{1}$
$= 2 P_{0}$

Q. Gas at a pressure P0​ is contained in a vessel . If the masses of all the molecules are halved and their speeds are doubled, the resulting pressure P will be equal to

4P0​

2P0​

P0​

2P0​​