Talk:Fundamental thermodynamic relation

Combined law of thermodynamics

(added from Talk:Laws of thermodynamics)

We don't have an article on the combined law of thermodynamics. Should it go here? -- Kjkolb 12:45, 1 December 2005 (UTC)

This is presently part of the Thermodynamic potentials article under "fundamental equations", but yes, it is in a way the most fundamental of the fundamental equations and should be mentioned here. PAR 04:02, 2 December 2005 (UTC)

Added to page per request (I've seen this version used as well).--Sadi Carnot 02:21, 5 April 2006 (UTC)

Corrected some serious errors

I suggest we give a proper rigorous derivation starting from the microcanocal ensemble. Count Iblis (talk) 18:32, 29 April 2008 (UTC)

dE?

Most authors usually use dU for the infinitesimal of internal energy. —Preceding unsigned comment added by 92.236.96.97 (talk) 09:59, 12 June 2008 (UTC)

Yes that's right, but then it doesn't really matter what symbol you use. Count Iblis (talk) 20:03, 12 June 2008 (UTC)

While it is true that the symbols used doesn't matter as long as you are consistent, it is rather important in this case for clarity's sake. The article refers to dE as an "infinitesimal change in internal energy." dE is used for a change in total energy in the system — potential, kinetic, and internal. But since the article is clear in its definition and consistent, I don't see a need to change it.TroyHaskin (talk) 15:30, 19 August 2009 (UTC)

obsolete terminology

This article says that the second law of thermodynamics is $dS=\delta Q/T$, but this appears to be archaic and nonstandard nomenclature (according to the wiki page for the second law of thermodynamics, Clausius called this equation the "second fundamental theorem in the mechanical theory of heat", but all modern source I've ever seen, including Wikipedia, say that the second law of thermodynamics is $\Delta S$ ≥ 0 or equivalent.)76.120.154.6 (talk) 01:02, 1 December 2008 (UTC)

I changed it by bypassing this issue. The lead was also affected, I made the statemtns there a bit more rigorous. Count Iblis (talk) 14:41, 1 December 2008 (UTC)

Better; but the article could be improved by giving references to reliable sources, other than someone's self-published lecture notes. The stat mech derivation reminds me of Kittel and Kromer's presentation of pressure: is that the source? 76.120.154.6 (talk) 15:15, 6 December 2008 (UTC)

The source is my own derivation. It is based on a derivation given in the book by F. Reif. But Reif's derivation (or, for that matter, any other derivation given in textbooks) cannot be copied here as it assumes that the reader has read the previous chapters of the book. Count Iblis (talk) 11:41, 5 January 2009 (UTC)

Might still be useful to reference Reif in one way or another then. I am quite happy I looked here and found these comments, they give me all the more motivation to read Reif's book. — Preceding unsigned comment added by 188.66.92.220 (talk) 19:54, 10 January 2014 (UTC)

Meaningless statement?

Does this mean anything?

"In a consistent unit system like the SI system the corresponding equation for the numerical values of the physical quantities relative to the unit system is of the same form."

Are there "inconsistent" unit systems? If you used one, would "the corresponding equation for the numerical values of the physical quantities" be different? What on Earth could this mean?

Is this like some Engineer's language -- as in, if you measure the volume in cubic feet, the pressure in mmHg, and the temp in °F, then you'll need all sorts of bizarre conversion factors? But, … this would apply to every single physically meaningful equation on Wikipedia.

I'm taking it out; someone else can tell me why it's important to leave in, and then they can put it back.

Thanks! — gogobera (talk) 22:17, 24 May 2010 (UTC)

I agree with taking the sentence out as you did. What happened was that someone included the list of SI units for the quantities in the equation, like E is the energy in Joules, etc. etc. But then that would be misleading, as the equation is valid in any system of consistent unit system, not just in the SI units. Consistent means, as you correctly note, that the physical quantities are expressed in mutual consistent units so that no extra conversion factors appear in the equations.

Now, you could argue that the SI unit system itself is not consistent because we know that time intervals and distances are different components of a unified space-time. So the speed of light is also a bizarre conversion factor that should be put equal to 1 by choosing consisent units for time intervals and distances. The same is true for inverse lengths and masses by putting hbar = 1. Finally, by putting G = 1 one can make everything dimensionless. Count Iblis (talk) 22:50, 24 May 2010 (UTC)

Why not use the natural logarithm?

Shouldn't this article use $k_{\mathrm {B} }$ and $\operatorname {ln}$ for the fundamental definition of entropy and not $k$ and $\operatorname {log}$? Kmarinas86 (Expert Sectioneer of Wikipedia) ^{19+9+14 + karma = 19+9+14 + talk = 86} 11:21, 20 January 2011 (UTC)

In the scientific literature and most university textbooks the natural logarithm is denoted by "$\operatorname {log}$". You can argue that $k$ should be $k_{\mathrm {B} }$, but you can also argue that $k$ is preferable because there is degree of freedom to define the temperature while by fixing $k=k_{\mathrm {B} }$ you make a definite choice. E.g. the book by Reif choses $k$ to be an arbitrary but dimensionless constant, so in that book $k$ is not $k_{\mathrm {B} }$. This means that temperature and energy have the same dimensions in Reif's book. Count Iblis (talk) 14:00, 20 January 2011 (UTC)

Connection with similar equations from other parts of physics (canonical transformation,GR)

I think it would be beneficial to add a little subsection named "Connections with other physics" or something like that. The equation $dU=TdS-pdV$ can be thought of as a canonical transformation from $(p,V)$ to $(T,S)$ coordinates of a phase space with $U$ as a generating function, similar to as how is the generating function approach to canonical transformations $dS=pdQ-PdQ$.

Also we can connect it to the black hole thermodynamics and the equation: $dE={\frac {\kappa }{8\pi }}\,dA+\Omega \,dJ$ and we see that all three equations are of similar form. 188.129.87.85 (talk) 15:28, 22 June 2024 (UTC)

But I will not make any edits before I get some feedback from someone more experienced. — Preceding unsigned comment added by 188.129.87.85 (talk) 18:58, 22 June 2024 (UTC)