Question

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

• A. $ 4\,P_0 $
• B. $ 2\,P_0 $
• C. $ P_0 $
• D. $ \frac{p_0}{2} $

Answer 1

Answer: (B)

The pressure $p$ extorted by a perfect gas on the walls of the containing vessel is given by
$ p = \frac{1}{3} \frac{mnc^2}{v}$
According to the question,
$P = P_0$
$m = m_0$
where, $n = $ number of molecules
$c =$ speed of molecules
According to question,
$m' = \frac{m_{0}}{2}$
$c' = 2c $
$ p' = p'_{0} $
$ P'_{0} = \frac{1}{3}\left(\frac{m_{0}}{2}\right)\times n\times \left(2c\right)^{2} $
$ = \frac{1}{3} m_{0}nc^{2} \cdot 2 $
$= p_{0} \times 2 $
$ = 2 p_{0}$