(i).Mean free path Iis directly proportional to the mass of the gas molecule. 1\(\times\)m
(ii) 1\(\times\)\(\frac{1}{p}\); p - density of the ga
(iii) 1\(\times\)\(\frac{1}{d^2}\); d - molecular diameter.
(iv) 1\(\times\)T; T - absolute temperature of the gas
(v) \(\lambda \times \frac { 1 }{ p } \); p - pressure of the gas.

(i) As we go up in the atmosphere, the number of air molecule per unit volume decreases.
(ii) The quantity of heat per unit volume or the heat density is low.
(iii) But the translational K.E per molecule is quite large. As the temperature is the measure of K.E, so temperature is high in the upper atmosphere but one feels cold due to low heat density.
(iv) Accumulate to the law of equipartition of energy average energy of each molecule =\(\frac{f}{2}\)K_BT.
(v) \(\therefore\) Internal energy of one molecule of the gas.
U = \(\frac{f}{2}\)K_BT.T\(\times\)NA =\(\frac{f}{2}\)RT
C_r = \(\frac{du}{dt}\)=\(\frac{f}{2}\)R
C_p = C_r+R
= \(\frac{f}{2}\)R + R = R\(\left( \frac { f }{ 2 } +1 \right) \)
\(\gamma =\frac { { C }_{ p } }{ { C }_{ v } } =\frac { \left( \frac { f }{ 2 } +1 \right) R }{ \frac { f }{ 2 } R } =1+\frac { 2 }{ f } \)
\(\therefore \gamma =1+\frac { 2 }{ f } \)

Consider one mole of a gas.
p - pressure; v - volume; T - temperature;
M - molecular mass of the gas; density p.
Accumulate to kinetic theory, the pressure excited by the gas is
v = \(\frac{1}{3}\)pc² = p =\(\frac{1}{3}\)\(\frac{m}{3}\).c2 (or) pv = \(\frac{1}{3}\)Mc²....(1)
pv = \(\frac{2}{3}\).\(\frac{1}{3}\)Mc²
\(\frac{1}{2}\)Mc². is the ave. K.E.E of one mole of the gas.
\(\therefore\) pv =\(\frac{2}{3}\) .E 
The ideal gas eqn for one mole of a gas is
pv = RT \(\therefore\) RT  = \(\frac{2}{3}\) E   (or) E=\(\frac{3}{2}\).RT
The above equation gives the mean K.E of one mole of gas.
\(\therefore\)The mean K. E per molecule is proportional to the absolute temperature of the gas.

Accumulate to kinetic theory:
(i) The molecules of a gas are in a state of continuous random motion. 
(ii) They collide with one another and also with the walls of the vessel. Whenever a molecule collides with the wall. It returns with a changed momentum and an equal momentum is transfused to the wall (conservation of momentum).
Accumulate to Newton's law:
(i) The transfer of momentum to the wall is equal to the force excited on the wall.
(ii) The force excited per unit area of the wall is the pressure of the gas.
Hence a gas excites pres due to the continuous call of its molecules with the walls of the vessel.

(i) A gas which obeys the ideal gas equation pv = nRT, at all temperature and pressure is called an ideal or perfect gas.
(ii) Following two assumptions are used to drive the ideal gas equation.
(iii) The size of the gas molecules is negligibly small.
(iv) There is no force of attraction amongst the molecules of a gas.
(v) No real or actual gas fulfills the above conditions. Hence the behaviour of a real gas differs from that of an ideal gas.
(vi) At low pressure and high temperature the above assumptions are valid and some real gases like H_2' O_2' N_2, H etc. almost behave like an ideal gel.