What is Entropy And How To Derive It By Using Clausius Law?

ENTROPY

Entropy is defined as disorder or randomness in any system. It is denoted by S. Entropy is the property of the scheme. It is an EXTENSIVE PROPERTY. Entropy depends on the state of the system ( state means a condition of the regime at a particular time). As long as a state of the system is fixed, then the entropy of the system remains constant. Entropy is a point function, and it is exact differentiate.

The entropy of system can’t be defined individually, it is always taken as the difference of entropy between two different states. ENTROPY OF THE SYSTEM INCREASES WITH INCREASES OF TEMPERATURE BECAUSE RANDOMNESS OF MOLECULES INCREASES WITH INCREASE OF TEMPERATURE.

The entropy of the system can be proved by Clausius inequality law. Which says that

Cyclic ∫(dq∕T) ≤ 0.    ( for reversible process ∫dq/T=0 and for irreversible process ∫dq/T<0

Now this quantity (dq∕T) is known as randomness or entropy of the system. Which is denoted by ds.  Now if u remove integration u can write     ∆S = Q/T. 

NOTE : Above equation of entropy is only valid for reversible process. For irreversible process this equation will become as follow ∆S>Q/T. (This proof can be obtained by Clausius inequality theorem).derivation of entropy equation for reversible and irreversible processes from Clausius inequality law

Þ     As we all know that friction is the main cause of irreversiblity And if there is friction then there is always generation of heat. Due to this heat, temperature raises so as entropy of the system. so here there is generation of extra entropy due to friction. This extra entropy is know as ∆S_generation.

Þ     Unlike entropy this quantity ∆S_{generation  ­}is not property of the system because ∆S_generation depends on path ( if path is reversible then u won’t get ∆S_generation. It is only valid if path/ process is irreversible). So it is a path function and inexact differential

Þ     ∆S_generation ≥0 always. If ∆S_generation<0 then process is not possible. If the process is reversible then ∆S_generation =0

In our universe all processes are irreversible process so entropy of universe always increases.