Two containers are at the same temperature. The first contains a gas with pressure $P_{1}$ , molecular mass $M_{1}$ and rms speed $v_{r m s_{1}}$ . The second contains gas with pressure $15 P_{1}$ , molecular mass $m_{2}$ , and average speed $V_{a v g 2} = 2.0 v_{r m s_{1}}$ . What is the ratio $m_{1} : m_{2}$ ?

Q. Assertion :In equation

P = \frac{1}{3} α v_{r m s}^{2}

, the term

α

represents density of gas. Reason:

v_{r m s} = \sqrt{\frac{3 R T}{M}}

Q. The curve between

v_{r m s}^{2}

and pressure

P

for constant volume is

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A gas mixture consists of molecules of type 1, 2 and 3, with molar masses m1>m2>m3. Vrms and ¯K are the r.m.s speed and average kinetic energy of the gases :

The correct option is A (Vrms)1<(Vrms)2<(Vrms)3 and ¯(K)1 =¯(K)2 =¯(K)3Vrms ∝ 1√M (from standard result)⇒ (Vrms)1<(Vrms)2<(Vrms)3 also in the mixture temperature of each gas will be same, hence kinetic energy also remains same

A gas mixture consists of molecules of type 1, 2 and 3, with molar masses $m_{1} > m_{2} > m_{3} .$ $V_{r m s}$ and $¯ K$ are the r.m.s speed and average kinetic energy of the gases :