1. The cohesive force (which binds molecules together) between particles of matter which constitutes a gas is extremely small.
2. Mathematical basis of Kinetic Theory of gases was established by Maxwell and Clausius.
3. Kinetic theory of gases relates macroscopic properties with microscopic properties of its molecules.
According to this theory,
4. Molecules are rigid, perfectly elastic and identical in all respects.
5. The average distance traveled by a molecule between two collisions is known as Mean free path.
6. On the basis of kinetic theory of gases, the pressure exerted by a gas is given by
P = (1/3)*(m*n*c²/)/V
where, 'n' is no. of moles, 'm' is mass of each molecule and 'M' is total mass of gas, V is volume of gas, c is average speed of molecules, c² is Mean square speed of molecules
c² = (c₁² + c₂² + .......+ cn²)/n
7. Pressure exerted by a gas 'P' is 2/3rd of total translational Kinetic energy of molecules per unit volume.
8. Mean kinetic energy of a molecule is
(1/2)mc² = (3/2)KT
where 'K' is Boltzmann Constant, K=R/NA ; R is universal gas constant & NA is Avagadro's number.
9. Kinetic energy of a gram molecule of a gas = (3/2)RT
10. Avogadro's Number
The number of atoms or molecules in a mole of substance is called Avogadro's number.
Its value is 6.023 x 10²³ mol⁻¹ .
11. Kinetic energy of a molecule depends upon absolute temperature 'T' and it is quite independent of its mass. This fact is known as Kinetic interpretation of temperature.
12. According to kinetic theory of gases, at absolute zero of temperature, the Kinetic Energy of gas becomes zero i.e. molecular motion ceases.
13. Above point is strictly not true because at T=0, the molecules do have some energy known as Zero Point energy.
14. Deduction of gas laws from kinetic theory:
i) Boyles law
P = (1/3)*Mc² ; PV=constant;
At constant temperature, pressure of a gas is inversely proportional to volume of a gas.
ii) Charles Law
PV ∝T ; The volume of gas at constant pressure is directly proportional to the temperature (or) pressure of a gas at consatnt volume is directly proportional to temperature.
iii) Avogadro's law
N1=N2; Equal volume of ideal gases existing under same conditions of temperature and pressure contain equal number of molecules. This is called as Avogadro's law.
iv) Dalton's law or partial pressure
P=P1+P2+ ....
the total pressure exerted by gaseous mixture is sum of individual pressures that would be exerted if several gases occupied space in turn, alone.
v) Grahams law of diffusion
The rate of diffusion of a gas through a porous portion is inversely proportional to square root of its density.
Root mean square velocity (crms) = √c² = √(3KT)/m = √(3P)/ρ
15. Law of equipartition of energy (deduced by James Clark Maxwell)
i) Average value of the components of velocity 'C' (i.e. u,v & w) along 3 directions should be equal or for a molecule all 3 directions are equivalent i.e. u=v=w
ii) Total mean kinetic energy of molecule is E = (3/2)KT;
K is Boltzman constant and T is absolute temperature.
iii) A molecule has "three translational" degrees of freedom.
iv) Total Kinetic Energy of a dynamical system is equally divided among all its degree of freedom and it is equal or (1/2)KT per degree of freedom.This is called Law of eqipartition of energy.
v) For a "monoatomic molecule", we have only translational motion because they are not capable of rotation. Thus for one molecule of a monoatomic gas total energy E=(3/2)KT.
vi) For a "diatomic molecule" we can suppose it to be two sphere joined by a rigid rod. Such a molecule can rotate about any one of 3 mutually perpendicular axes. The rotational inertia about an axis along rigid rod is negligible compared to that about an axis perpendicular to rod, so rotational energy consists of to terms such as (1/2)I𝓌y² & (1/2)I𝓌z².
vii) For special description of center of mass of a diatomic gas molecule, 3 coordinates will be required. Thus, for a diatomic gas molecule having both rotational & translational motion;
E = (3/2)KT + 2(1/2)KT = (5/2) KT
viii) For "tri-atomic gases", each molecule contains 3 spheres joined together by rods so that molecule is capable of rotating energetically 3 mutually perpendicular axes. Hence, for triatomic molecule having both translational & rotational motion energy 'E' will be
E = 3(1/2)KT + 3(1/2)KT = 3KT
ix) If a molecule in all has 'f' degrees of freedom, its average total energy would be (1/2)fKT.
