Changes in Entropy
Posted: Sun Jan 22, 2017 11:55 pm
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.
Re: Changes in Entropy
Posted: Mon Jan 23, 2017 12:15 am
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)