study material-physics-thermodynamics

# Gas Laws - 3

__VI. Kinetic Molecular Theory of Gases__:

(a) __Postulates__:

(i) Molecules of gas are separated from each other by large distance so, actual volume of molecule is negligible as compared to total volume of gas.

(ii) Distance of separation between molecules are so large that of attraction are negligible.

(iii) Molecules are perfectly elastic. So, no wastage ……. energy during collision.

to absolute temperature of gas.

__Kinetic Gas Equation__

PV = mnu^{2}

P Pressure exerted by gas.

v Volume of gas

m Mass of each molecule of gas

n Total no. of molecules

u Root mean square speed of gas

For 1 mole, m x n = mass of 1 mole

= M Molar mass in gm

PV = MV^{2}

densityof gas.

__Most Probable Speed__: This is speed possessed by max. fraction of molecules.

__RMS Speed__: It is square root of mean of square of speeds of molecules.

RMS =

__Average speed__: It is average of different speeds of all molecule.

Average speed =

__RMS Speed__: U =

__Most Probable Speed__:

__Average Speed__: V =

: v : u = 1 : 1.128 : 1.224 |

PV = mnu

^{2}= (mn = M Total mass of gas)

But Mu

^{2}= K.E. of gas

PV = K.E. ……………………………………….. (i)

K.E. Absolute Temperature (T)

K.E. = KT

Putting in eq.(i)

PV = KT

As K is constant. So, if T is constant, KT will be constant.

PV = constant |

(Boyle’s law)

©

__Charle’s law__:

PV = KT

If P is constant, then

Charle’s law

(d)

__Relation between Average Kinetic Energy & Absolute Temperature Kinetic Gas Equations__:

According to kinetic gas equation

Pv = mnv

^{2}………………………………………… (i)

Pv = Mv

^{2}(M = m x n) ……………………………. (ii)

Pv =

Pv = K.E.

K.E. = Pv for 1 mole of gas …………………………….. (iii)

Putting this in eq. (iii)

K.E. = RT for 1 mole

Avg. K.E. of 1 molecule =

Boltzmann constant.

i.e.

__Illustration__: At 27

^{0}C, a gas contains 10 molecules travelling with speed of 4 m/s, 20 molecules travelling with speed of 5 m/s & 40 molecules travelling with speed 8 m/s. Calculate Avg. speed, RMS speed & Most probable speed & Molarmass of gas ?

Ans: Avg. speed (u

_{av}) = = 6.56

RMS (v

_{rms}) = = 6.78

Most probable speed = 0.816 x v

_{rms}= 0.816 x 6.78 = 5.53 m/s

M = = 163.1 amv