From 689382af7776257acd32bb8e6608e2161d6143aa Mon Sep 17 00:00:00 2001 From: Indigo5684 <159226326+Indigo5684@users.noreply.github.com> Date: Tue, 30 Sep 2025 13:19:35 -0500 Subject: [PATCH] Thermal Physics Fix --- docs/physics/thermal/2-second-law.md | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/docs/physics/thermal/2-second-law.md b/docs/physics/thermal/2-second-law.md index cdeaacd..ca010c0 100644 --- a/docs/physics/thermal/2-second-law.md +++ b/docs/physics/thermal/2-second-law.md @@ -82,7 +82,7 @@ Note that this is not a rigorous proof, and we have not shown that there are no Now, consider a two-molecule system. As we only fix total kinetic energy, the momentum constraint thus becomes $p_{1x}^2 + \ldots + p_{2x}^2 + \ldots = 2mU$, assuming both molecules have the same mass. Then, we can write -$$\Omega_2 = \frac{V^2}{h^6} \cross \text{area of momentum 6-dimensional sphere}$$ +$$\Omega_2 = \frac{V^2}{h^6} \times \text{area of momentum 6-dimensional sphere}$$ This only holds true, however, if the two molecules are somehow distinguishable. In reality, molecules are indistinguishable and swapping the two molecules will not yield a distinct state. Thus, we have over-counted by a factor of 2.