Statistical Interpretation of Entropy By:- Rama Arora Associate Professor Govt. College for Girls Sector 11, Chandigarh

Statistical Definition of Entropy Statistically the Entropy S of a system is the product of the natural logarithm of thermodynamics probability W and Boltzmann Constant k S = k lnW (k = 1.38 x 10-16 erg/K) So Entropy in the state of equilibrium of system is given by S = K ln (Wmax)

Change of entropy of a system The thermodynamic probability W is a function of no. of particles (n) (which is function of µ amount of substance, the total no. of available phase space cells (which in turn depends upon the volume) and the energy u of the system. S = f (u, v, µ) Therefore entropy s, is also a function of µ, v, u. So the entropy of the system can be changed by changing the energy µ.

First law of thermodynamics From first law of thermodynamics δQ = dU + PdV Since V is constant, so δQ = dU Since δQ is infinitesimally small so the system is assumed to be in most probable state ds = δQ /T

Additive Nature of Entropy S1 and S2 be entropies of the sub-systems A and B respectively. S = S1 + S2 In general, the entropy of the system is given by the summation of entropies of all the subsystems of the system. i.e. S = ∑ Si A B k i=1

Third law of thermodynamics Thermodynamics probability W decreases with the decrease of temp. The minimum possible temperature is called the absolute zero. S = k log W When W = 1, S=0. The absolute zero temperature is 00 kelvin

Reversible Process -> Carnot cycle A process in which a system can be retraced to its initial state by reversing the controlling factor is called reversible process. -> Carnot cycle

Irreversible Process Equilibrium Only At End of Process Physical Processes That Proceed in One Direction But Not The Other Tends Towards Equilibrium Equilibrium Only At End of Process ->Thermal Conduction Hot Cold dQ

Irreversible Processes Diffusion of gases

Principle of increase of entropy A natural process always takes place in such a direction as to cause an increase in the entropy of the system and surroundings. In an isolated system the entropy of the system always tends to increase.

Ice melting -an example of "entropy increasing"

Entropy and Disorder Entropy is a measure of molecular disorder. It is the law of the nature that disorder is more probable than order.

Is this your room/ Then you already know about entropy

A system (such as a room) is in a state of high entropy when its degree of disorder is high. As the order within a system increases, its entropy decreases.

Thanx !