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In the case of reversible process from initial state 'a' to final state 'b' ,one may define entropy

by

1) Constructing infinitely many reservoirs having temperatures corresponding to the temperature at every point on the P-V diagram of the process from 'a' to 'b'

2) Finding [itex]\frac{dQ}{T}[/itex] at every point

where dQ is the elemental heat transferred at every point,T is the corresponding temperature at the point.

3)Now by linking each reservoir of temperature T to a reservoir at unit absolute thermodynamic temperature by a reversible heat engine.

4) ∴ ,[itex]\frac{dQ}{T}[/itex] = [itex]\frac{Qs}{1}[/itex] = dS

5) Now integrating the entropy of every elemental part on the P-V curve,we get the total change in entropy as

ΔS = [itex]\int^{b}_{a}\frac{dQ}{T}[/itex]

(Abs. entropy can be determined using nernst theorem)

Similarly,how can we determine the entropy or change in entropy for a irreversible process.

Gentlemen,i would be happy if we stick to a thermodynamic approach rather than Quantum mechanical approach(of course unless it is necessary)

(My sincere Request:For god's sake, please don't talk about entropy as randomness)