Timeline for Statistical mechanics and Planck constant universality
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Sep 10, 2018 at 21:09 | comment | added | user196574 | I think I will need to refresh my knowledge on the chemical potential before returning to the role of $h$ in the grand canonical ensemble. Specifically, whether it is necessary to have some theoretical expression for $\mu$ (that depends on $h$) in order to be able to set $\mu$, or whether they may be ways to experimentally determine a chemical potential without knowledge of $h$, just as there are ways to experimentally determine a volume without knowledge of $h$. | |
| Sep 10, 2018 at 20:42 | comment | added | ACuriousMind♦ | @user196574 $\mu$ is fixed for a specific macrostate in the grand canonical example. It's a free parameter in the sense that derivations that are supposed to hold for a system must hold for all possible values of this parameter, just like they must hold for all values of $T$ and $V$ (that obey the equation of state). You can't just say "but $T = 1\mathrm{K}$ in my system". That's not a property of the system, but of a state of the system. In any experimental test, you would have to establish that indeed $\mu = 0$ for the state you're measuring, thus losing the ability to measure $h$. | |
| Sep 10, 2018 at 20:03 | comment | added | user196574 | Also, there are cases where nature "fixes" $\mu$ and not number of particles, the classic example being a photon gas. However, we can even fix $\mu$ and not the number of particles by affixing our system to a "particle number" bath. This is how I think about it, please let me hear your thoughts: A heat bath can give heat without noticeably changing its temperature until an adjoined smaller system is at the same temperature. A particle number bath can give particles without noticeably changing its chemical potential until an adjoined smaller system is at the same chemical potential. | |
| Sep 10, 2018 at 19:59 | comment | added | user196574 | Thanks for the response. In the grand canonical ensemble, the fixed parameters are T, V, and $\mu$. The pressure and number of particles fluctuate because they are not fixed. I don't believe that $\mu$ is a free parameter. | |
| Sep 10, 2018 at 18:41 | history | answered | ACuriousMind♦ | CC BY-SA 4.0 |