**Entropy**:

The extent of disorder or randomness in a system may be expressed by a thermodynamic property known as **entropy**. Entropy may be defined as **the property of a system which measures the degree of disorder or randomness in the system.**

It is generally expressed by the symbol, **S**. Entropy like internal energy and enthalpy, is a state function and change in entropy, therefore, depends only on the initial and final states of the system. The change in entropy during the process when a system undergoes a change from one state to another is represented by ∆S. Thus,

∆S = S (final state) — S (initial state) and for chemical reactions,

∆S = S (products) — S (reactants)

For chemical reactions, entropy change is attributed to the change in rearrangement of atoms or ions in the reactants to that in the products. If the structure of the products is very much disordered than that of the reactants, there will be resultant increase in entropy (∆S = +ve).

Entropy may also be related to the heat involved in a process. Whenever heat is added to the system, it increases molecular motion resulting increased randomness in the system. The distribution of heat also depends on the temperature at which heat is added to the system. A system at a higher temperature has greater randomness in it than at lower temperature. When heat is added to a system at lower temperature, it increases the randomness of the system to greater extent than when the same quantity of heat is added to it at a higher temperature. Thus, entropy change is inversely proportional to the temperature.

For a reversible process at equilibrium, the change in entropy may be expressed as:

∆S = q _{rev}/T

Where **q** represents the heat absorbed when the process is carried out reversibly and isothermally i.e. at constant temperature. Thus, **entropy change during a process may also be’ defined as the amount of heat absorbed isothermally and reversibly divided by the absolute temperature at which heat is absorbed. **

**Entropy as a state function**:

Consider a cylinder containing a gas fitted with a frictionless and weightless piston which is in contact with a large heat reservoir. Let us consider isothermal and reversible expansion of the gas from volume V_{1} to V_{2} and the substance absorbs heat q, at temperature T.

Change in entropy of the system, S _{sys} = q _{rev}/T

Since an equivalent amount of heat is lost by the reservoir and therefore, change in entropy of reservoir will be:

∆S_{ rev} = – q _{rev}/T

Minus sign indicates that heat is lost by the reservoir to the system.

Total entropy change may be written as:

∆S_{1} = ∆S _{sys}+ ∆S _{res}

= q _{rev}/T + (-q _{rev})/T = 0

Now, let us assume that we compress the gas thermally from a volume of V_{2} to V_{1} so that heat is given by the system is – q _{rev}. Therefore,

Change in entropy of the system, S _{sys} = – q _{rev}/T

Since reservoir has gained heat, change in entropy of reservoir is

∆S _{rev} = q _{rev}/T

Total change in entropy is:

∆S_{2} = ∆S _{sys} + ∆S _{rev}

= — q _{rev}/T + q _{rev/}T = 0

Thus, the total entropy change for the complete cycle is zero, i.e. ∆S_{1} + ∆S_{2} = 0

In other words, after the end of cycle, the entropy of the system is same as it had initially. Therefore, entropy is a state function.

As we have studied, the total entropy change (∆S _{total}) of system and surroundings of a spontaneous process is given as:

∆S total = ∆S sys + ∆S surr > 0

As we have learnt, in an isolated system such as mixing of gases, there is no exchange of energy or matter between the system and the surroundings. But due to increase in randomness, there is increase in entropy. Thus, we can say that for a spontaneous process in an isolated system, the change in entropy is positive i.e. ∆S > 0. However, if the system is not isolated, we have to take into account the entropy changes of the system and the surroundings. Then, the total entropy change (∆S total) will be equal to the sum of the change in entropy of the system (∆S _{sys}) and the change in entropy of the surroundings (∆S _{surr}) i.e.

∆S total = ∆S sys + ∆S surr

For a spontaneous process, ∆S total must be positive

∆S total = ∆S sys + ∆S surr > 0

But system and surroundings constitute universe for thermodynamic point of view so that for spontaneous change

∆S _{universe}>0

This led to the formation of second law of thermodynamics.