Time between successive collision on wall
Where, N= total number of particles, m=mass of each particle, C=rms (root mean square), V=volume.
= no. of particles per unit volume then,
Nm=M= total mass of gas then,
If E is the total kinetic energy of the gas molecules per unit volume.
Average kinetic energy per mole of the gas = =
Average kinetic energy per molecules of the gas = =
Where,k=is Boltzmann constant and it's value is
The average kinetic energy of the gas is directly proportional to the absolute temperature. If temperature is increased, the average kinetic energy of the molecule also increase. Thus, the temperature of the gas gives a measure of average kinetic energy of the gas.
Also, at absolute temperature, the molecules of the gas are at complete rest.
Degree of freedom of a system are defined as the total number of co-ordinates or independent quantities required to described the configuration of the system completely.
The average kinetic energy of a molecule of a gas is =
The average kinetic energy of a monoatomic molecule, in each degree of freedom is,
so, the molecule has kinetic energy per degree of freedom.
For diatomic gas, there is rotational and translation kinetic energy of the molecules. So, the rotational KE of a diatomic molecules is,
Average KE of monoatomic molecules= (trans.)
Average KE of diatomic molecules= (trans.)+ (rot.)=
Average KE of polyatomic molecules= (trans.)+ (rot.)=
It states that for a dynamical system in thermal equilibrium, the energy of the system is equally distributed amongst the various degrees of freedom and the energy associated with each degree of freedom per molecules is .
Mean free path of a molecule is defined as the average distance travelled by the molecule between two successive collisions and is measured as the mean of a large number of free path.