## Why are W and V interchangeable in the Boltzman formula?

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

Leo_Navejas_3B
Posts: 12
Joined: Wed Sep 21, 2016 2:58 pm

### Why are W and V interchangeable in the Boltzman formula?

In lecture we saw that $\Delta S= k_B R ln \frac{v_2}{v_1}$
So why is that the same as $\Delta S= k_B R ln \frac{W_2}{W_1}$ ?

mikezargari
Posts: 20
Joined: Wed Sep 21, 2016 2:56 pm
Been upvoted: 1 time

### Re: Why are W and V interchangeable in the Boltzman formula?

I believe because W is simply the number of different ways or combinations in which atoms can in a sense exist. Using that definition of W we can assume that if the volume has doubled then so have the number of different ways in which the atoms can orient themselves. If V2/V1 = 2/1 then W2/W1 = 2/1.

Sophia Rawson 1C
Posts: 12
Joined: Wed Sep 21, 2016 2:58 pm

### Re: Why are W and V interchangeable in the Boltzman formula?

I don't know that they will always be interchangeable but in the example given during lecture the degeneracy (W) was interchangeable with volume because he said that the volume doubled. Doubling the volume therefore making 2x the available positions. This means that V2/V1=2 and W2/W1 are both equal to 2.

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 2 guests