Re: [Phys-l] thermo differential and extensive/intensive variables

[Stefan Jeglinski <jeglin@4pi.com>]

(going backwards here)

> Here's my attempt to formulate thermodynamics without the usual
> hogwash:
>    http://www.av8n.com/physics/thermo-laws.htm

I was reading this, but missed a link to your partial derivatives 
page (maybe it's there) you also cited. So obviously, my example is 
doubly wrong:

E(S,T) -> dE = (dE/dS)(const T) dS + (dE/dT)(const S) dT = (!T)dS + (!Cv)dT

(! means "not")

>    Some peculiar things happens if *all* of the variables are intensive,
>    but other than that, you can choose any combination of intensive and
>    extensive variables.  Even the all-intensive case makes sense if you
>    are careful, and is actually kinda elegant.

So it might seem that the most general way of approaching thermo 
problems is to assume that all variables are always included, for 
example E = E(S,V,N,P,T), and an equation of state (eg PV=NkT). I 
haven't looked at this yet, but I don't recall thermo texts with this 
approach. At first glance it would appear that this approach would 
not lead to elegant relationships, but this may be a premature 
conclusion.

---------------

The reason I was reviewing this was to reconsider the simple 
heating/cooling of water (for example) without resorting to the dE = 
d'Q + d'W formulation, as per previous discussions here. To use J 
Denker's terminology, uncramped vs cramped (if I followed it 
correctly). But I'm finding the going tough. The standard treatment 
is simply "you heat the water, d'Q = CvdT, and if you want the 
entropy change, solve TdS = CvdT." My perhaps naive approach is to 
describe the process non-mathematically as

1. Add/remove energy to/from the water
2. Some of the energy goes to changing the entropy of the water
3. Some of the energy goes to changing the temperature of the water

I would then like to give this a more formal mathematical expression. 
Importantly, I would like it be valid for a phase change, during 
which all of the energy goes to changing the entropy, and none to 
changing the temperature.


Stefan Jeglinski