HSC Class 12 Physics: Kinetic Theory of Gases & Radiation | Complete Theory & PYQs ()

KINETIC THEORY OF GASES AND RADIATION


CONTENT AND CONCEPTS:

 Introduction  Specific Heat Capacity
 Behavior of a Gas  Absorption, Reflection &
 Ideal Gas and Real Gas Transmission of Heat Radiation
 Mean Free Path  Perfect Black body
 Root Mean Square (r.m.s) Speed  Emission of Heat Radiation
 Interpretation of Temperature in  Kirchhoff’s Law of Heat Radiation &
Kinetic Theory Radiation its Theoretical Proof
 Law of Equipartition of Energy  Spectral Distribution of Blackbody
 Stefan – Boltzmann Law of Radiation




INTRODUCTION:

The kinetic theory of gases was developed in 19th century by Maxwell, Boltzman and others. The main
aim of kinetic theory was to account quantitatively for the microscopic property of gas molecules [such
as speed, momentum, Force K.E of molecules etc] which relates with macroscopic property of gases
[such as pressure, volume, temperature etc] assuming that their (gas molecules) motions are described
by the laws of mechanics [usually classical Newtonian mechanics, although quantum mechanics is also
needed in some cases].

For any solid objects, the motion can be well described by the help of Newton’s Laws of motion.
Similarly, a gas enclosed in container can be characterized by macroscopic state variables like
pressure(P), volume(V) and temperature(T). However, as gas molecules are always in random motion,
it is difficult to understand behavior of a gas in terms of motion of single molecule and Since the number
of molecules in the gas is so large (=1023 molecules per m3) that motion of individual molecule cannot
be related with macroscopic parameters P,V,T and Energy. Hence it is necessary to make certain
assumption while studying behavior of gas.

Further, the gas pressure can be related directly to temperature and density and many other gross
properties of gas can also be derived such as viscosity, Thermal and electrical conductivity, diffusion ,
heat capacity and so on.

, Q . What are the properties of gases?

Properties of Gases:

In gases, the intermolecular forces are very weak and its molecules may fly apart in all directions.
So the gas is characterized by following properties:
1) It has no shapes and size and can be obtained in a vessel of any shape or size.
2) It expands indefinitely and uniformly to fill the available space.
3) It exerts pressure on its surroundings.
4) Intermolecular forces in a gas are minimum.
5) They can easily compress and expand.

Q. What are the Gas Laws?


Gas Laws: The laws that relates the pressure, volume and temperature of the gas are known as gas laws.

There are three basic gas laws.
1. Boyle’s Law [T = constant]

For a given fixed mass of an ideal gas at constant temperature, the volume of gas is inversely proportional to its pressure.

1
i.e. when T = constant Then V  or PV = constant or P1V1 = P2V2
P

 mass  m p p p
Also it can be written as, p   constant  p  = constant   constant  1  2
 density  ρ  1  2

2. Charle’s Law [ p = constant]:

For a given fixed mass of an ideal gas at constant pressure. The volume of gas is directly proportional to its absolute
temperature.
V V V
i.e. when p = constant then VT  constant  1  2
T T1 T2

3. Gay – Lussac’s Law : [V = constant ]

For Lussac’s fixed mass of an Ideal gas at constant volume. The pressure of gas is directly proportional to its absolute
temperature
P P
i.e. when V = constant Then p  T or  constant   constant
T T

,  Some important terms used for K.T.G.
1) Mole : One mole is the amount of a substance that contains as many particles as there are atoms in exactly 12g of the
carbon -12 isotopes
Mole No. of molecules Mole Mass of substance
1 6.023 x 1023 = NA 1 Molar mass = M0
n N n Given mass=M

N M
 (NA) (n) = (N) (1)  n   (M0) (n) = (M) (1)  n 
NA M0
2) Universal Gas Constant (R): we select the (R) value based on the units for the known quantities in the problem i.e.
 For (P) in Pa , use R = 8.31 J /(mol) (Kelvin)
 For (PV) in calories we use R = 1.98 cal / (mol) (Kelvin)
PV Energy
Dimension of (R): R    [R]  [M 1 L2 T 2 1 ]
nT Temp.

Note : There is difference between values of pressure and temperature at S.T.P [Standard temperature, pressure]
and N.T.P [Normal Temperature, pressure]
At S. T. P. P = 1bar = 1 atm = 105Pa T = 00C = 273 k

At N.T.P. P = 1.0132 x 105 Pa T = 200C = 293 K (Room Temp.)

3) Boltzman constant (K)
R 8.31 Joule
 {no of molecules in 1 mole is NA = 6.023 x 1023}
N A 6.023 10 Kelvin
23


 K = 1.38 x 1023 J/K
This (K) is called Boltzman constant which represent gas constant(R) per mole
R PV 1 Energy
Dimension of (K): K      [K] = [M1L2T21]
NA T NA Temp

Q Derive Ideal gas Equation.
Ideal gas Equation or Equation of state
The relation between three variables of a gas i.e. pressure, volume and absolute temperature is called Ideal gas
Equation or equation of state of gas.
For a given fixed mass (M) of 1 mole of an enclosed gas,
1
from Boyle’s Law at constant temperature, V  --------------------- (1a)
P
From Charle’s Law, at constant pressure, V  T ----------------------- (1b)
T T
From Equation (1a) and (1b) we can write V or V = (constant)
P P
PV
  constant (R) Thus PV=RT------------------------ (1c)
T
Note : Since the state of any gas is specified by a number of physical quantities such as (P) , (V) and (T)
Therefore The equation relating these quantities is known as Equation of state.