> Q. If average velocity becomes 4 times then what will be the effect on rms velocity at that temperature? – LIVE ANSWER TODAY

Q. If average velocity becomes 4 times then what will be the effect on rms velocity at that temperature?

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If average velocity becomes 4 times then what will be the effect on rms velocity at that temperature?

Solution:

Key Idea Ratio of $ {{v}_{av}}/{{v}_{rms}} $ remains constant. Average speed is the arithmetic mean of the speeds of molecules in a gas at a given temperature, ie, $ {{v}_{av}}=({{v}_{1}}+{{v}_{2}}+{{v}_{3}}+…)/N $ and according to kinetic theory of gases, $ {{v}_{av}}=sqrt{frac{8RT}{Mpi }} $ ?(i) Also, rms speed (root mean square speed) is defined as the square root of mean of squares of the speed of different molecules, ie, $ {{v}_{rms}}=sqrt{(v_{1}^{2}+v_{2}^{2}+v_{3}^{2}+…)/N} $ $ =sqrt{{{(overline{v})}^{2}}} $ and according to kinetic theory of gases, $ {{v}_{rms}}=sqrt{frac{3RT}{M}} $ ?(ii) From Eqs. (i) and (ii), we get $ {{v}_{av}}=sqrt{left( frac{8}{3pi } right)}{{v}_{rms}} $ $ =0.92,{{v}_{rms}} $ ?(iii) Therefore, $ frac{{{v}_{av}}}{{{v}_{rms}}}= $ constant Hence, root mean square-velocity is also become 4 times.

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