- Products of complete combustion (PCC) are useful for simple calculations.
- Can be considered an upper bound on the extent of reaction.
- Useful for defining heating values and providing a combustion basis.
- At high temperatures products dissociate to form $H_2$, $CO$, $H$, $O$, $OH$, etc.
Criteria for equilibrium
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Consider a fixed mass at equilibrium
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$dU = dQ + dW$
- $dW = -PdV$
- at equilibrium differential changes are reversible, so $dQ = TdS$.
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$dU = TdS - PdV$
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Assume const $T$ and $P$, then we can move $T$ and $P$ inside the derivatives:
- $dU = d(TS) - d(PV)$.
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Collect terms:
- $d(U+PV-TS) = d(H-TS)= dG = 0$.
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At equilibrium $$dG_{T,P} = 0$$
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Hence $G$ is a critical point.
- When not at equilibrium changes are not reversible and $dS > dQ/T$ so $dQ < TdS \rightarrow dG<0$,
- Hence $G$ is a minimum at equilibrium.
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Note equilibrium is a state not a process.
- The $T,P$ in $dG_{T,P}=0$ does not mean that that the equilibrium applies to a constant $T$ and $P$ process.
- Rather, if you look in directions of constant $T$ and $P$, then the $G$ curve will be minimum at the equilibrium point.
Other equivalent equilibrium conditions
- Above, we had
$$dU = TdS - PdV$$
- For constant $T$, $P$, we have $dG_{T,P}=0$.
- For constant $S$, $V$, we have $dU_{S,V}=0$.
- For constant $S$, $P$, we have $dU=-d(PV)\rightarrow dH_{S,P}=0$.
- For constant $T$, $V$, we have $dU=d(TS)\rightarrow dA_{T,V}=0$, where $A$ is Helmholz free energy.
- All of these four expressions are true of an equilibrium state at a given temperature and pressure.
- Similarly, all of these four expressions are true at a given $S$ and $V$, etc.
- Again, this is because equilibrium is a state, not a process.