Timeline for Equilibrium between a system and a heat reservoir
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 18 at 15:09 | comment | added | Jbag1212 | @ApoorvMishra They are talking about a specific microstate, so $\Omega (E_r) =1$ | |
| Apr 18 at 6:49 | comment | added | Apoorv Mishra | @Jbag1212 Can you explain your edit? Because I think the probability should be proportional to the product of those Microstates. | |
| Aug 15, 2023 at 19:55 | comment | added | Jbag1212 | "One can explicitly calculate this value in microcanonical framework" - the reservoir here is supposed to be completely general. Therefore, I do not see how you can say that its value can be explicitly calculated. My concern is that if $\Omega(E) \sim E^N$ then it does not also seem like $\Omega(E) \sim \exp(\beta E).$ $E^N$ and $e^{(cE)}$ are differently behaving functions. | |
| Aug 13, 2023 at 8:05 | comment | added | user35952 | @Jbag1212 Have you stumbled upon this notes (itp.uni-frankfurt.de/~gros/Vorlesungen/TD/…), they present a fairly lucid explanation of canonical ensemble | |
| Aug 13, 2023 at 8:03 | comment | added | user35952 | @Jbag1212 I am sorry, but I don't clearly understand your concern. Here, $\Omega(E)$ concerns the total number of microstates for a given macrostate of energy $E$. One can explicity calculate this value in microcanonical framework and obtain that $\Omega(E) \sim E^N$. Would you mind clarifying your question again? | |
| Aug 10, 2023 at 21:59 | comment | added | Jbag1212 | Is it more accurate to say that $\Omega(E)$ scales as $\exp(-\beta E)$? Then $d \ln \Omega / d E = \beta$ for some constant $\beta.$ The conclusion reached that $P_r \propto \Omega \propto \exp(-\beta E)$ is equivalent to assuming that the expansion of the logarithm is a "good" expansion. But assuming that $\Omega(E) \propto E^N$ implies that $P_r \propto \exp(N \ln(E))$. Asserting that $P_r \propto \exp( E \cdot (n \ln(E)/E)$ where $\beta = n \ln(E)/E$ seems strange. | |
| Aug 9, 2023 at 19:56 | comment | added | Jbag1212 | Nevermind, I was just misreading. I thought they were asserting $P_S \propto \Omega_S$, but they were really asserting $P_S \propto \Omega_R$ for a particular microstate. | |
| Aug 9, 2023 at 12:28 | comment | added | Jbag1212 | Yes, sorry, I forgot that wasn’t included in the OP. The $’$s in general refer to the reservoir, and unprimed is the system in equilibrium with the reservoir. | |
| Aug 9, 2023 at 5:54 | comment | added | user35952 | @Jbag1212 May I know what is the difference between $\Omega$ and $\Omega'$? | |
| Aug 8, 2023 at 19:40 | comment | added | Jbag1212 | Thanks, please see my edit too. | |
| Dec 8, 2022 at 23:04 | vote | accept | Jbag1212 | ||
| Dec 8, 2022 at 5:21 | history | answered | user35952 | CC BY-SA 4.0 |