Physics class 11

CHAPTER - 13

KINETIC ENERGY

• BOYLE's LAW:- It states that at a constant temperature, volume of given mass of gas is inversely proportional to its pressure.

                                          v ~ 1\p

                                  or PV= constant

 

• CHARLES LAW:- It states that at constant pressure, the volume of a given mass of gas is directly proportional to its absolute temperature.

                                                       V~T

                                             or V\T = constant

• GAY LUSAC"S LAW:- It states that at constant volume, the pressure of a given mass of gas is directly proportional to its absolute temperature.

                                                              P~T

                                                 or, P\T = constant

For 1 degree Celsius rise in a temperature,

P(t) = P(b) (1 + t/273.15)

• IDEAL GAS EQUATION:- For 'n' mole of gas, 

                                            PV = nRT

for 1 mole, PV= RT

UNI.VERSAL GAS CONSTANT, 

R = 8.31 J 1/mol 1/K

BOLTZMANN CONSTANT,

Kb = R/Na

Na -> AVAGADRO'S NO.

• IDEAL  GAS:- A gas that obeys gas law strictly is an ideal or perfect gas. The molecules of such gas are of point size and there is no force of attraction between them.

• ASSUMPTION OF KINETIC THEORY OF GASES:-

1.  all gases consist of molecules that are rigid, elastic spheres identical in all respect for a given gas.
2. the size of a molecule is negligible as compared with the average distance between two molecules.
3. diving the random motion, the molecules collide with each other and with the wall of a vessel. The collisions are almost instantaneous 
4. the molecular density remains uniform throughout the gas
5. the collisions are perfectly elastic in nature and there are no forces of attraction or repulsion between them. 

• LAW OF EQUIPARTITION OF ENERGY

For any thermodynamical system in thermal equilibrium, the energy of the system is equally divided into its various degree of freedom, and the energy associated with each degree of freedom corresponding to each molecule is 1/2KbT, where Kb is the BOLTZMANN'S CONSTANT  and T is the absolute temperature.

The law of equipartition of energy holds a good for all degrees of freedom whether translational, rotational, or vibrational.

A monoatomic gas molecule has only translational kinetic energy.

Ex + Er = 1/2mv(x)*2 + 1/2mv(y)*2 + 1/2mv(z)*2 + 3/2.2KbT

So, a monoatomic gas molecule has only three degrees of freedom.

In addition to a translational kinetic energy, a diatomic molecule has two rotational kinetic energies.

E(t) + E(r) = 1/2mv(x)*2 + 1/2mv(y)*2 + 1/2mv(z)*2 + 3/2.2KBT

                                ◯一◯

Here the line joining the two atoms has been taken x-axis about where there is  no rotation, So, the degree of freedom of a diatomic molecule is 5, it does not vibrate.

At a very high temperature, vibration is also activated due to which two extra degrees of freedom emerge from vibrational energy. Hence, at very high temperature degree of freedom of diatomic molecule is seven.

• PRESSURE EXERTED BY AN IDEAL GAS

P = 1/3e⊽*2

or, P = 1/3 nM⊽*2

where P = Pressure

           n = number density (no. of molecules/volume)

           M = mass of one molecule

           ⊽^2 = square mean speed

   also called kinetic gas eqn.

• MEAN K.E PER MOLECULE OF GAS

E = 1/2m⊽^2

or, E = 3/2 KbT

• DALTON'S LAW OF PARTIAL PRESSURE

It states that total pressure of a mixer of non-reacting ideal gas is the sum of partial pressure exerted by individual gases in the mixture.

P = p1+p2+p3+....................+pn

• GRAHAMIC LAW OF DIFFUSION

It states that the rate of diffusion of a gas to inversely proportional to the square root of its density.

                      r~1/r√⍴

Graham's Law = r1/r2 = √⍴2/√⍴1

• SPEEDS OF THE GASES

Average Speed

v= √8RT/πM

or, v = √8PV/πM

or, v = √8KbT/πM  m/s

Root Mean Square Speed

Ⅴrms= √3RT/M

or, Vrms = √3RV/M m/s

or, Vrms = √3KbT/M

MOST PROBABLE SPEED

Vmp =√2RT/M

or, Vmp = √2PV/m

or, Vmp = √2KbT/M

  DEGREES OF FREEDOM   

The total number of co-ordinates of independent quantities required to describe completely position and configuration of a dynamical system is known as number of degrees of freedom of the system.

                                f= 3N-K

N = no. of molecules

K = no. of co-ordinates of the particle

For monoatomic, f=3

        diatomic, f=5

        triatomic (linear motion), =7

        triatomic (non-linear motion), =6

MEAN FREE PATH

It is the average distance travelled by a molecule between two successive collisions. It is denoted by λ.

                            λ= 1/mπd*2

      

d= diameter of each molecule

m= no. of molecules per unit volume

                               λ= KbT/√2πd*2P

SPECIFIL HEAT CAPACITY

Average energy of a molecule at temp. T = 3/2KbT

total internal energy of a mole of such a gas is,

                                           U= 3/2KbT
                                             Na=3/2RT

molar specific heat at constant volume Cv(monoatomic gas)= 

                                                  dv/dt = 3/2RT

For an ideal gas,

                                            Cp - Cv = R
                                               Cp = 5/2R

Ratio of specific heats,

                                                Cp/Cv = 5/3

DIATOMIC GASES

A diatomic molecule has 5 degree of freedom : 3 transitional and 2 rotational,

                                      U = 5/2KbT, Na = 5/2RT

Cv (rigid diatomic) = 5/2R

                                Cp = 7/2R

rigid diatomic = 7/5

POLYATOMIC GASES

Polyatomic molecule has 3 translational, 3 rotational and a certain number (f) of vibrational modes.

                           V = (3/2KbT + 3/2KbT + fKbT)Na

                              Cv = (3+f)R, Cp = (4+f)R

Note :- Cp -Cv = R  is true for any ideal gas.

BROWNIAN MOTION

It is a zig-zag motion of the particle of microscopic size suspended in water, air, or some other fluid. This motion can be explained on the basis of K.T.

It depends upon :-

1. size of suspended particle
2. 'f' of fluid
3. temperature of medium
4. viscosity of the medium

LINK TO THIS CHAPTER'S YOUTUBE VIDEO:- https://youtu.be/voNdPhHOfVI