It is that gas which strictly rules the gas laws:
(i) The size of the molecule of a gas is zero i.e. every molecule of a gas is a point mass with no dimensions.
(ii) There is no force of repulsion or attraction amongst the molecules of the gas.
All real gases are not perfect gases as they do not rule gas law perfectly. However at extremely low pressure and high temperature some perfect gases like hydrogen, nitrogen, oxygen, helium etc. obey the gas rules a fair degree of accuracy and hence behaves as nearly perfect gases.
Pressure Due to Ideal Gas:
P = (1/3mn/V)v2rms [P = pressure, V = volume, m = mass of each molecule, n = no. of molecules in gas]
P = (1/3M/V)v2rms [ = Root mean square velocity, M = Total mass of the gas, M = m × n]
P = (1/3ΡV)v2rms [Ρ=M/V = density of the gas]
Kinetic Energy of Ideal gas:
(i) Mean kinetic energy of 1 mole of gas E = (3/2)RT.
(ii) Mean kinetic energy of 1 molecule of gas E = (3/2)KT .
(iii) Mean kinetic energy of 1 gram of gas E = (3/2)rT
These expressions are valid only for mono atomic gases. It has 3 degree of freedom.
General expression (if gas posses f degree of freedom)
E = ( f /2)RT [for 1 mole of gas], E = ( f /2)RT[for 1 molecule of gas], E = ( f /2)RT[for 1 gm. of gas]
Relation between pressure and kinetic energy :
Mean Kinetic energy of unit volume of gas E = 1/2Ρv2rms and P = (1/3ΡV)v2rms . From above two equations P=(2/3)E
That means the pressure operated by an ideal gas is numerically equal to two third of the mean kinetic energy of translation per unit volume of the gas.
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