From 96447d884e02012a4ed9146dc6c00d186a201038 Mon Sep 17 00:00:00 2001 From: Prefetch Date: Sun, 21 Jul 2024 17:52:57 +0200 Subject: Improve knowledge base --- .../know/concept/laws-of-thermodynamics/index.md | 104 --------------------- 1 file changed, 104 deletions(-) delete mode 100644 source/know/concept/laws-of-thermodynamics/index.md (limited to 'source/know/concept/laws-of-thermodynamics') diff --git a/source/know/concept/laws-of-thermodynamics/index.md b/source/know/concept/laws-of-thermodynamics/index.md deleted file mode 100644 index 3605a0e..0000000 --- a/source/know/concept/laws-of-thermodynamics/index.md +++ /dev/null @@ -1,104 +0,0 @@ ---- -title: "Laws of thermodynamics" -sort_title: "Laws of thermodynamics" -date: 2021-07-07 -categories: -- Physics -- Thermodynamics -layout: "concept" ---- - -The **laws of thermodynamics** are of great importance -to physics, chemistry and engineering, -since they restrict what a device or process can physically achieve. -For example, the impossibility of *perpetual motion* -is a consequence of these laws. - - -## First law - -The **first law of thermodynamics** states that energy is conserved. -When a system goes from one equilibrium to another, -the change $$\Delta U$$ of its energy $$U$$ is equal to -the work $$\Delta W$$ done by external forces, -plus the energy transferred by heating ($$\Delta Q > 0$$) or cooling ($$\Delta Q < 0$$): - -$$\begin{aligned} - \boxed{ - \Delta U = \Delta W + \Delta Q - } -\end{aligned}$$ - -The internal energy $$U$$ is a state variable, -so is independent of the path taken between equilibria. -However, the work $$\Delta W$$ and heating $$\Delta Q$$ do depend on the path, -so the first law means that -the act of transferring energy is path-dependent, -but the result has no "memory" of that path. - - -## Second law - -The **second law of thermodynamics** states that -the total entropy never decreases. -An important consequence is that -no machine can convert energy into work with 100% efficiency. - -It is possible for the local entropy $$S_{\mathrm{loc}}$$ -of a system to decrease, but doing so requires work, -and therefore the entropy of the surroundings $$S_{\mathrm{sur}}$$ -must increase accordingly, such that: - -$$\begin{aligned} - \boxed{ - \Delta S_{\mathrm{tot}} = \Delta S_{\mathrm{loc}} + \Delta S_{\mathrm{sur}} \ge 0 - } -\end{aligned}$$ - -Since the total entropy never decreases, -the equilibrium state of a system must be a maximum -of its entropy $$S$$, and therefore $$S$$ can be used as -a [thermodynamic "potential"](/know/concept/thermodynamic-potential/). - -The only situation where $$\Delta S = 0$$ is a reversible process, -since then it must be possible to return to -the previous equilibrium state by doing the same work in the opposite direction. - -According to the first law, -if a process is reversible, or if it is only heating/cooling, -then (after one reversible cycle) the energy change -is simply the heat transfer $$\dd{U} = \dd{Q}$$. -An entropy change $$\dd{S}$$ is then expressed as follows -(since $$\ipdv{S}{U} = 1 / T$$ by definition): - -$$\begin{aligned} - \boxed{ - \dd{S} - = \Big( \pdv{S}{U} \Big)_{V, N} \dd{U} - = \frac{\dd{Q}}{T} - } -\end{aligned}$$ - -Confusingly, this equation is sometimes also called the second law of thermodynamics. - - -## Third law - -The **third law of thermodynamics** states that -the entropy $$S$$ of a system goes to zero when the temperature reaches absolute zero: - -$$\begin{aligned} - \boxed{ - \lim_{T \to 0} S = 0 - } -\end{aligned}$$ - -From this, the absolute quantity of $$S$$ is defined, otherwise we would -only be able to speak of entropy differences $$\Delta S$$. - - - -## References -1. H. Gould, J. Tobochnik, - *Statistical and thermal physics*, 2nd edition, - Princeton. -- cgit v1.2.3