Degree of Freedom, Specific Heat Capacity & Mean Free Path | Physics for JEE Main & Advanced PDF Download

Degree of Freedom

The degree of freedom for a dynamic system is the number of directions in which it can move freely or the number of coordinates required to describe completely the position and configuration of the system.

It is denoted by for N.

Degree of freedom of a system is given by

f or N = 3A – R

where A = number of particles in the system and R = number of independent relations.

Degree of Freedom

1. For monatomic gas = 3
2. For diatomic gas = 5
3. For non-linear triatomic gas = 6
4. For linear triatomic gas = 7

 Specific heat of a gas

(a) At constant volume, C_V = f/2 R

(b) At constant pressure, c_p = (f/2 + 1)R

(c) Ratio of specific heats of a gas at constant pressure and at constant volume is given by
γ = 1 + 2/f

Mean Free Path

The average distance travelled by a molecule between two successive collisions is called mean free path (γ).

Mean free path is given by

γ = kT / √2 π σ²p

where σ = diameter of the molecule, p = pressure of the gas,
T = temperature and k = Botlzmann’s constant.

Mean free path

λ ∝ T and λ ∝ 1/p

Brownian Motion

The continuous random motion of the particles of microscopic size suspended in air or any liquid, is called Brownian of microscopic motion.

Brownian suspended motion in both is observed with many liquids and gases.

Brownian motion is due to the unequal bombardment of the suspended Particles by the molecules of the surrounding medium.