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Entropy Change for an Irreversible Process

Path A is irreversible and
path B is

internally reversible

This is great for reversible processes, but what about real, irreversible processes?

Changes in

state variables

do not depend on the process path.

Entropy

, S, is a state variable.

Therefore, ΔS is the same for both path A (irreversible) and path B (internally reversible).

PV diagram showing two reversible paths, A and B, from state 1 to state 2.

Lesson
7B Blog

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Lesson 7B: page 5 of 21

What is the relationship between DS from state 1 to state 2 along a reversible path and ΔS from state 1 to state 2 along an irreversible path ?
Well, because entropy is a STATE variable, changes in entropy do not depend on the process path.
This means that ΔS for an irreversible path is the same as DS for an internally reversible path.
That is great, but I want to caution you.
This does NOT mean that the integral of dQ over T is the same for an irreversible path as it is for an internally reversible path !
Don’t get confused. Remember that dQ over T is ONLY a state variable when it is evaluated along an internally reversible path.
For an irreversible process, ΔS must be evaluated along a HYPOTHETICAL, internally reversible path.
This can be confusing. Play this mini-lecture again if you need to.
When you are ready, flip the page and we’ll talk about how to evaluate changes in enthalpy for non-isothermal processes.

Entropy Change for an Irreversible Process

internally reversible

state variables

Entropy

Ch 7, Lesson B, Page 5 - Entropy Change for an Irreversible Process