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+---
+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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