Definition of Entropy for Irreversible Processes

[Hummel]

What is the definition of entropy of a thermodynamic irreversible process?

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 $\frac{dQ}{T}$ 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) ∴ ,$\frac{dQ}{T}$ = $\frac{Qs}{1}$ = dS

5) Now integrating the entropy of every elemental part on the P-V curve,we get the total change in entropy as
ΔS = $\int^{b}_{a}\frac{dQ}{T}$

(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)

 

[Jano L.]

Entropy has meaning only for equilibrium states. If we have some process (does not matter whether it is reversible or not) that takes the system from the state $A$ to state $B$, the change in entropy is

$$
\Delta S = S(B) - S(A).
$$

So, we need to know the states A,B and their entropy.

 

[SW VandeCarr]

What is the definition of entropy of a thermodynamic irreversible process?

It's the same as for a reversible process as far as I know. While the entropy of an irreversible process can't be calculated directly, the change in entropy a is state function independent of path, so one should be able calculate $\Delta S$ by approaching the problem as if the process were reversible.

http://www.files.chem.vt.edu/chem-dept/marand/set6.pdf

 

[Hummel]

Entropy has meaning only for equilibrium states. If we have some process (does not matter whether it is reversible or not) that takes the system from the state $A$ to state $B$, the change in entropy is

$$
\Delta S = S(B) - S(A).
$$

So, we need to know the states A,B and their entropy.

Sir,my question was how do you define entropy for irreversible process?
apart from that,How do you determine S(B) and S(A)?

 

[Hummel]

It's the same as for a reversible process as far as I know. While the entropy of an irreversible process can't be calculated directly, the change in entropy a is state function independent of path, so one should be able calculate $\Delta S$ by approaching the problem as if the process were reversible.

http://www.files.chem.vt.edu/chem-dept/marand/set6.pdf

I totally appreciate the PDF attachment.
I will get back once i completely go through it and if if we have to iron out any kinks.

 

[Chestermiller]

If the initial and final equilibrium states for the irreversible process are well defined, you need to dream up (i.e., conceive of) a reversible process that gets you between these same two equilibrium states, and use that process to calculate the change in entropy.

Chet