Question

At a pressure of 24 x 100000 dyne/cm², the volume
of nitrogen gas is 5litre and mass is 20gm. The 'rms
velocity will be in m/sec)
​

Answer 1

Answer: 1341.64 m/sec

Step by Step Solution:-

Given,

Pressure of gas(P) = 24 × 10⁵ dyne/cm²

Volume of gas(V) = 5 litre  = 5000 ml

Mass of gas(m) = 20gm

We know that by gas equation

PV = μRT,

Where μ is number of moles of gas.

If M is molecular weight of gas then,

μ = m/M

M = m/μ

We know that,

$v_{rms}=\sqrt{\frac{3RT}{M}}\\\;\\v_{rms}=\sqrt{\frac{3RT}{\frac{m}{\mu}}}\\\;\\v_{rms}=\sqrt{\frac{3\mu RT}{m}}\\\;\\v_{rms}=\sqrt{\frac{3PV}{m}}\\\;\\v_{rms}=\sqrt{\frac{3\times24\times10^5\times5000}{20}}\\\;\\v_{rms}=\sqrt{\frac{3\times24\times5\times10^8}{2}}\\\;\\v_{rms}=\sqrt{3\times12\times5\times10^8}\\\;\\v_{rms}=6\sqrt{5}\times10^4\;\;cm/s\\\;\\v_{rms}=6\sqrt{5}\times10^2\;\;m/s\\\;\\v_{rms}=1341.64\;\;m/s$

Note:- We have changed all quantity in C.G.S. as force is given in C.G.S. For making calculations easy