ENTROPY

 History 

The concept of entropy was introduced into the study of thermodynamics by Rudolph Clausius in 1856 to give a quantitative basis for the second law. 

State Variable 

It provides another variable to describe the state of a system to go along with pressure, volume, temperature and internal energy. If a system undergoes a reversible process during which it absorbs a quantity of heat ∆Q at absolute temperature T, then the increase in the state variable called entropy S of the system is given by 

Like potential energy or intemal energy, it is the change in entropy of the system which is important.

Positive Entropy 

Change in entropy is positive when heat is added and negative when heat is removed from the system. 

Explaination 

Suppose, an amount of heat Q flows from a reservoir at temperature T1 through a conducting rod to a reservoir at temperature T2 when T1 > T2. The change in entropy of the reservoir, at temperature T1, which loses heat, decreases by Q/T1 and of the reservoir at temperature T2, which gains heat, increases by Q/T2. 

As T1 > T2 so Q/T2 will be greater than Q/T1

i.e.

Q/T2 > Q/T1 

Hence, 

Net change in entropy = Q/T2 - Q/T1 is positive

Another statement of 2nd law of thermodynamics 

In all natural processes where heat flows from one system to another, there is always a net increase in entropy. This is another statement of 2nd law of thermodynamics. According to this law 

Statement:

"If a system undergoes a natural process, it will go in the direction that causes the entropy of the system plus the environment to increase."

Relation between entropy and molecular disorder

It is observed that a natural process tends to proceed towards a state of greater disorder. Thus, there is a relation between entropy and molecular disorder. 

For example: An irreversible heat flow from a hot to a cold substance of a system increases disorder because the molecules are initially sorted out in hotter and cooler regions. This order is lost when the system comes to thermal equilibrium. Addition of heat to a system increases its disorder because of increase in average molecular speeds and therefore, the randomness of molecular motion. 

Similarly, free expansion of gas increases its disorder because the molecules have greater randomness of position after expansion than before. Thus in both examples, entropy is said to be increased.

Conclusion 

We can conclude that only those processes are probable for which entropy of the system increases or remains constant. The process for which entropy remains constant is a reversible process; whereas for all irreversible processes, entropy of the system increases.

Entropy and work done 

Every time entropy increases, the opportunity to convert some heat into work is lost. For example there is an increase in entropy when hot and cold waters are mixed. Then warm water which results cannot be separated into a hot layer and a cold layer. There has been no loss of energy but some of the energy is no longer available for conversion into work. 

Therefore, increase in entropy means degradation of energy from a higher level where more work can be extracted to a lower level at which less or no useful work can be done. The energy in a sense is degraded, going from more orderly form to less orderly form, eventually ending up as thermal energy.

In all real processes where heat transfer occurs, the energy available for doing useful work decreases. In other words the entropy increases. Even if the temperature of some system decreases, thereby decreasing the entropy, it is at the expense of net increase in entropy for some other system. When all the systems are taken together as the universe, the entropy of the universe always increases.