249 reputation
19
bio website
location Brisbane
age
visits member for 2 years, 11 months
seen Aug 19 at 6:16

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.


15h
awarded  Popular Question
Aug
12
accepted Why doesn't Euler's theorem provide an *absolute* energy scale
Aug
12
comment Why doesn't Euler's theorem provide an *absolute* energy scale
Ahh, OK, I think I understand: classical thermodynamics is consistent without assuming the 3rd law. Thanks for your help, I think this makes sense now :)
Aug
10
comment Why doesn't Euler's theorem provide an *absolute* energy scale
OK, the more I think about this the more it makes sense: if we add even one more atom, how do we quantify the energy added? For instance, do we count relativistic mass-energy or not? It's impossible to define exactly how much energy we've added, without of course having a reference state telling us how much energy is in a mole of some state of matter. Still not sure on the entropy question though :)
Aug
10
comment Why doesn't Euler's theorem provide an *absolute* energy scale
Sorry, one more question. It seems natural to me that the difference in energy between a 1L balloon and a 2L balloon with the same composition is well defined. But according to what you've said this doesn't seem to be the case. If the 1L is said to have 1kJ of energy the 2L will have 2 kJ, and the difference will be 1kJ, but if the 1L is said to have 3kJ of energy the 2L will have 6 kJ, and the difference will be 4kJ. This is unintuitive to me (I feel this internal energy difference should be well defined) but am I correct to reason that this energy difference is in fact not well defined?
Aug
10
comment Why doesn't Euler's theorem provide an *absolute* energy scale
To emphasize this again, I can develop an experimental method for measuring $S$, by starting at 0 Kelvin and adding energy and monitoring the temperature increase and evaluating $S= \int_0^{T_f} dQ/T $. There's no change in $N$ here, and we only need to measure energy flow and temperature, both of which are absolute. How then isn't entropy 'measurable' like pressure or volume?
Aug
10
comment Why doesn't Euler's theorem provide an *absolute* energy scale
One question though - you say entropy, energy and chemical potential are relative. I am under the impression entropy has a well defined zero, precisely when the temperature is 0. I see now that adjusting $U$ to $U+N\alpha $ changes $N \mu$ and $U$ in the same way, so that $U= TS - PV + \mu N$ holds after the change. So $\mu$ is relative, but I still don't see why $S$ isn't absolute, and how I can change $S$ in a system by fiddling with the relative nature of $U$.
Aug
10
comment Why doesn't Euler's theorem provide an *absolute* energy scale
Thanks, I came to a similar conclusion after a little more thought: the relative state is literally that - a state defined say by a temperature and pressure but whose size may vary to be the size of the system we're interested in. I was imagining a box with a fixed amount of energy to which we compared all systems to.
Aug
4
asked Why doesn't Euler's theorem provide an *absolute* energy scale
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?