## Changes in Entropy

$\Delta S = \frac{q_{rev}}{T}$

Oyindamola Akinnusi 2A
Posts: 2
Joined: Wed Sep 21, 2016 2:58 pm

### Changes in Entropy

In the text book (p.323), it shows how the derivation for the dependence of entropy of an ideal gas on its volume when expansion is isothermal. How does does nRT come into play when calculating for work? I understand the ln(V2/V1), but I am confused on how -nRT is brought about.

Yiling Liu 1N
Posts: 25
Joined: Sat Jul 09, 2016 3:00 am

### Re: Changes in Entropy

This is how I interpreted it:

The textbook mentions work in two primary ways - one is work at a constant pressure, and the other is work when pressure is not constant.

Since chapter 9 typically deals with reversible processes, then the work involved is reversible work where external pressure is not constant.

In this case:

W = Fd
W = - Pa * d
W = -P* change in volume

But again, for reversible processes, we can't just substitute in a value for external pressure if it's not constant, so we further derive the equation:

dW = -P * dv
dW = -nRT/v * dv ............ (knowing PV=nRT)
Taking the integral of both sides
W = -nRT * ln (v2/v1)