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Diffstat (limited to 'source/know/concept/laws-of-thermodynamics/index.md')
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1 files changed, 15 insertions, 15 deletions
diff --git a/source/know/concept/laws-of-thermodynamics/index.md b/source/know/concept/laws-of-thermodynamics/index.md index 7758446..3605a0e 100644 --- a/source/know/concept/laws-of-thermodynamics/index.md +++ b/source/know/concept/laws-of-thermodynamics/index.md @@ -19,9 +19,9 @@ is a consequence of these laws. 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 ($\Delta Q < 0$): +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 ($$\Delta Q < 0$$): $$\begin{aligned} \boxed{ @@ -29,9 +29,9 @@ $$\begin{aligned} } \end{aligned}$$ -The internal energy $U$ is a state variable, +The internal energy $$U$$ is a state variable, so is independent of the path taken between equilibria. -However, the work $\Delta W$ and heating $\Delta Q$ do depend on the path, +However, the work $$\Delta W$$ and heating $$\Delta Q$$ do depend on the path, so the first law means that the act of transferring energy is path-dependent, but the result has no "memory" of that path. @@ -44,9 +44,9 @@ the total entropy never decreases. An important consequence is that no machine can convert energy into work with 100% efficiency. -It is possible for the local entropy $S_{\mathrm{loc}}$ +It is possible for the local entropy $$S_{\mathrm{loc}}$$ of a system to decrease, but doing so requires work, -and therefore the entropy of the surroundings $S_{\mathrm{sur}}$ +and therefore the entropy of the surroundings $$S_{\mathrm{sur}}$$ must increase accordingly, such that: $$\begin{aligned} @@ -57,19 +57,19 @@ $$\begin{aligned} Since the total entropy never decreases, the equilibrium state of a system must be a maximum -of its entropy $S$, and therefore $S$ can be used as +of its entropy $$S$$, and therefore $$S$$ can be used as a [thermodynamic "potential"](/know/concept/thermodynamic-potential/). -The only situation where $\Delta S = 0$ is a reversible process, +The only situation where $$\Delta S = 0$$ is a reversible process, since then it must be possible to return to the previous equilibrium state by doing the same work in the opposite direction. According to the first law, if a process is reversible, or if it is only heating/cooling, then (after one reversible cycle) the energy change -is simply the heat transfer $\dd{U} = \dd{Q}$. -An entropy change $\dd{S}$ is then expressed as follows -(since $\ipdv{S}{U} = 1 / T$ by definition): +is simply the heat transfer $$\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{ @@ -85,7 +85,7 @@ Confusingly, this equation is sometimes also called the second law of thermodyna ## Third law The **third law of thermodynamics** states that -the entropy $S$ of a system goes to zero when the temperature reaches absolute zero: +the entropy $$S$$ of a system goes to zero when the temperature reaches absolute zero: $$\begin{aligned} \boxed{ @@ -93,8 +93,8 @@ $$\begin{aligned} } \end{aligned}$$ -From this, the absolute quantity of $S$ is defined, otherwise we would -only be able to speak of entropy differences $\Delta S$. +From this, the absolute quantity of $$S$$ is defined, otherwise we would +only be able to speak of entropy differences $$\Delta S$$. |