In a vessel, the gas is at pressure P_0. If the mass of all the molecules is halved and their speed is doubled, then the

Q: In a vessel, the gas is at pressure $P_0$. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

b $P = \frac{1}{3}\frac{{mN}}{V}v_{rms}^2$ $P \propto m\,v_{rms}^2$so $\frac{{{P_2}}}{{{P_1}}} = \frac{{{m_2}}}{{{m_1}}} \times {\left( {\frac{{{v_2}}}{{{v_1}}}} \right)^2} = \frac{{{m_1}/\,2}}{{{m_1}}}{\left( {\frac{{2\,{v_1}}}{{{v_1}}}} \right)^2} = 2$ ==> ${P_2} = 2{P_1} = 2{P_0}$

SECTION - A [PHYSICS MCQ]

GSEB - English Medium

In a vessel, the gas is at pressure $P_0$. If the mass of all the molecules is halved and their speed is doubled, then the resultant pressure will be

A$4{P_0}$
B$2{P_0}$
C${P_0}$
D$\frac{{{P_0}}}{2}$

Medium

STD 11 Science
JEE
STD 11 - 12 . kinetic theory of gases
Physics

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