232 reputation
18
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location Brisbane
age
visits member for 2 years, 10 months
seen Jul 11 at 7:54

I'm an undergraduate Engineering/Mathematics Student down in Brisbane, Australia. Interested in learning as much as I possibly can about maths, particularly the ideas/constructions/history/motivation behind the classic undergraduate concepts.


Jul
2
awarded  Curious
Apr
2
asked Boltzmann distribution: derivation from canonical distribution
Mar
1
awarded  Popular Question
Feb
4
awarded  Popular Question
Dec
22
awarded  Nice Question
Oct
5
awarded  Yearling
Jun
15
comment Which formula for entropy is correct? (OR Is the fundamental thermodynamic equality always right?)
Sorry, did you mean the second equation is more general (considering you derived it)? :)
Jun
15
accepted Which formula for entropy is correct? (OR Is the fundamental thermodynamic equality always right?)
Jun
15
comment Which formula for entropy is correct? (OR Is the fundamental thermodynamic equality always right?)
Thankyou very much, that's fantastic, and makes 100% sense :) I must admit I'm slightly disturbed by your reply though, considering that in a 3rd year chemical engineering course we have freely been using the first equation with EOS's like $P = \frac{RT}{V-b}-\frac{a}{\sqrt{T}V_m(V_m+b)}$ (a common EOS called the Reidlich-Kwong EOS) which certainly doesn't obey your criterion :(
Jun
13
awarded  Commentator
Jun
13
comment Which formula for entropy is correct? (OR Is the fundamental thermodynamic equality always right?)
BTW - how do you know $P$ is a function of $T$ and $U$ in the second equation? Why not $S$ or another thermodynamic quantity?
Jun
13
comment Which formula for entropy is correct? (OR Is the fundamental thermodynamic equality always right?)
That's a fascinating idea - pressure is defined by this relation (is there a particular text that presents thermodynamics that way?) I haven't actually encountered a derivation for the first equation anywhere, indeed I don't know of a textbook that gives it. I can tell you we need to use the first equation when given an equation of state of the form $P = f(T,\underline{V})$ (the simplest of which is the ideal gas law). So you might be onto something ...
Jun
13
asked Which formula for entropy is correct? (OR Is the fundamental thermodynamic equality always right?)
Mar
20
comment Using 'Euler's Homogeneous Function Theorem' to Justify Thermodynamic Derivations
@DaniH Yes, I may have made a mistake here. Euler's theorem is invoked in the integration of the internal energy formula on this page, and I, perhaps incorrectly, extrapolated this logic to the similar - looking gibbs-free energy derivation.
Mar
20
asked Using 'Euler's Homogeneous Function Theorem' to Justify Thermodynamic Derivations
Mar
7
accepted Is a world with constant/decreasing entropy theoretically impossible?
Feb
3
answered Gauge pressure vs. absolute pressure?
Feb
2
comment Is a world with constant/decreasing entropy theoretically impossible?
I've heard this before, and I guess you're technically right - if we could 'create' a universe in the exact state as our universe and then reverse the motion of all the atoms/charges/forces, etc, then it should run according to relatively familiar laws, except that entropy would constantly be decreasing. Admittedly this is extremely Laplacian, and I'm not sure if quantum mechanics has anything to say on the matter...
Feb
2
asked Is a world with constant/decreasing entropy theoretically impossible?
Jan
25
comment Generalisation of Reversible Equation to Non-Reversible Situations Because it Only Contains 'Properties of the System'
Thanks for your help, I do really appreciate it, but I'm still not 110% satisfied with your logic. Perhaps could you point out what's wrong with this 'counter-example'. There's a class of reversible processes (in particular, adiabatic ones) which, on top of obeying the complex equation above, also obey the simpler $dS=0$. Now we know that $S$ is a state function, so why can't we use the same logic and say that, just because $dS=0$ holds for all adiabatic, reversible processes, it must hold for all adiabatic processes, including irreversible ones (obviously ridiculous)? Thanks