Question

Explains the different types of speed possessed by molecules ​

Answer 1

There are basically three different types of molecular speed - Root mean square speed, average speed and most probable speed.

Vʳᵐˢ =

$\sqrt{3rt} \\ m$

1) Root mean square speed

It is the square root of the mean of the squares of the speeds of different molecules.

Formula for Root mean square speed, 'v ':

2) Average Speed

It is the arithmetic mean of the speeds of different molecules.

Formula for average velocity, 'v ':

3) Most Probable Speed

It is the speed possessed by maximum number of molecules of the gas.

Formula for Most probable speed, 'v ':

where,

R = Gas constant

M = Molar mass of the gas

T = temperature of the gas.

ᴵ ᴴoᵖe ᵗʰiˢ ᴴeˡᵖˢ ⓤ

Answer 2

${\huge {\mathfrak {\orange {Answer :-}}}}$

${\mathfrak {\pink {-:Molecular \: Velocity :-}}}$

$<b>$ In kinetic theory of gas the velocity of molecules is expressed in the following three terms

➡️ (i) Root-mean square velocity or R.M.S. Velocity:

It may be defined as, “The square root of the mean value of the squares of the velocities of all molecules”. It is denoted by u. If V_1, V_2, V_3, \cdots V_n are the velocities for n molecules, then u = \sqrt{\dfrac{V_1^2 + V_2^2 + V_3^2 + \cdots + V_n^2}{n}}

➡️ (ii) The average velocity is the arithmetic mean of the velocities of all molecules. It is denoted by v and is given by the following equation:

v = \dfrac{(V_1 + V_2 + V_3 + \cdots V_n)}{n}[

Average velocity (v) = 0.9213 x R. M. S. velocity (u)

➡️ (iii) The most probable velocity is the velocity possessed by maximum number of molecules of the gas at a given temperature. It is denoted by \alpha and is given by the following equation:

\alpha = \dfrac{2RT}{M} = \dfrac{2RT}{mN} (since M= mN)

Or,

\alpha = \sqrt{\dfrac{2u}{3}}

These three velocities are related to each other as:

Y : v : \alpha = 1.0 : 0.9213 : 0.8177

\alpha = 1.0 : 1.128 : 1.224 so \alpha < v < u

Maxwell’s distribution of velocities.

Refer above ⬆️ ⬆️ in attachment. $</b>$

$<i>That's it..$

${\red {-:Arnab \: here :-}}$
$<marquee>$
${\huge {\blue {Thanks}}}$