## The overall change in Entropy [ENDORSED]

Boltzmann Equation for Entropy: $S = k_{B} \ln W$

Sophia Kim 1C
Posts: 51
Joined: Fri Sep 29, 2017 7:04 am
Been upvoted: 1 time

### The overall change in Entropy

In section 9.10 in the textbook it states that since deltaU = q+w it follows that q rev must be greater than q irrev because only than can the sums of q and w be the same for the two paths. Can someone explain what that means?

Chem_Mod
Posts: 18400
Joined: Thu Aug 04, 2011 1:53 pm
Has upvoted: 435 times

### Re: The overall change in Entropy  [ENDORSED]

Not only does qrev need to be greater than qirrev but also for wrev must be greater than wirrev. Note that here we mean greater in absolute terms, you must consider the signs depending on whether work is done by or work is done on the system. This is simply because following the reversible path gives you the maximum amount of work a system can do or have done on it.

Since the change in internal energy U is a state function, it should be same for whether an irreversible or reversible path was taken. Try solving for q and w in the reversible and irreversible case between the same two states of a gas (T, V, n, P) to confirm this and develop your intuition.

Return to “Third Law of Thermodynamics (For a Unique Ground State (W=1): S -> 0 as T -> 0) and Calculations Using Boltzmann Equation for Entropy”

### Who is online

Users browsing this forum: No registered users and 1 guest