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From: Prefetch
Date: Sun, 21 Jul 2024 17:52:57 +0200
Subject: Improve knowledge base

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----
-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.
-- 
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