Since molecules move at random, the average kinetic energy correspoonding to each degree of freedom is the same. According to kinetic theory of gases, the mean kinetic energy of a molecule is 3/2 kT. Each molecule has 3 degrees of freedom due to translatory motion. Let us consider one mole of a monoatomic gas in thermal equilibrium at temperature T. The energy associated with each degree of freedom per moelcule is ½ kT, where k is the Boltzmann’s constant. Law of equipartition of energy states that for a dynamical system in thermal equilibrium the total energy of the system is shared equally by all the degrees of freedom. The vibratory motion of the molecules has not been taken into consideration. In all the above cases, only the translatory and rotatory motion of the molecules have been considered. Therefore, it possesses three degrees of freedom of rotation in addition to three degrees of freedom of translation along the three co-ordinate axes Hence it has six degrees of freedom Examples : molecules of H 2O, SO 2, etc. Triatomic molecule (Non-linear type)Ī triatomic non-linear molecule may rotate, about the three mutually perpendicular axes, as shown in figure. It, therefore, behaves like a diamotic moelcule with three degrees of freedom of translation and two degrees of freedom of rotation, totally it has five degrees of freedom as shown in figure. In the case of triatomic molecule of linear type, the centre of mass lies at the central atom. Examples: molecules of O 2, N 2, CO, Cl 2, etc. So, a diatomic molecule has five degrees of freedom as shown in figure. Hence it has two degrees of freedom of rotational motion in addition to three degrees of freedom of translational motion along the three axes. The diatomic molecule can rotate about any axis at right angles to its own axis. Since a monoatomic molecule consists of only a single atom of point mass it has three degrees of freedom of translatory motion along the three co-ordinate axes as shown in figure.Įxamples : molecules of rare gases like helium, argon, etc. The rotatory motion also can have three co-ordinates in space, like translatory motion Therefore a rigid body will have six degrees of freedom three due to translatory motion and three due to rotatory motion. A rigid body with finite mass has both rotatory and translatory motion. (e.g) a bird that flies.Ī point mass cannot undergo rotation, but only translatory motion. (c) A particle moving in space (X, Y and Z axes) has three degrees of freedom. (b) A particle moving in a plane (X and Y axes) has two degrees of freedom. (a) A particle moving in a straight line along any one of the axes has one degree of freedom (e.g). The number of degrees of freedom of a dynamical system is defined as the total number of co-ordinates or independent variables required to describe the position and configuration of the system. Concepts of Physics by HC Verma for JEE.IIT JEE Coaching For Foundation Classes.

Degrees of freedome