1.14.60: Second Law of Thermodynamics
The Second Law introduces an extensive function of state, a property of a given system, called the entropy , symbol \(\mathrm{S}\).
Spontaneous chemical reaction in a closed system is driven by the affinity for spontaneous change \(\mathrm{A}\) producing a change in chemical composition \(\xi\). The change in entropy \(\mathrm{dS}\) at temperature \(\mathrm{T}\) is given by Equation \ref{a}.
\[\mathrm{T} \, \mathrm{dS}=\mathrm{q}+\mathrm{A} \, \mathrm{d} \xi \label{a} \]
where
\[\mathrm{A} \, \mathrm{d} \xi>0 \label{b} \]
The latter inequality is the LAW. This inequality is the key to chemistry. In effect the law states that if there is an affinity for a given chemical reaction ( i.e. a driving ‘force’ for reaction) the chemical reaction will spontaneously proceed in that direction. This is the thermodynamic selection rule for which there are no exceptions.
In the limit that a system undergoes a ‘reversible ‘ change, \(\mathrm{A}\) is zero; the system is at equilibrium with the surroundings. For a reversible change
\[\mathrm{T} \, \mathrm{d} \mathrm{S}=\mathrm{q} \label{c} \]
Often texts seek to answer the question ‘what is entropy?’ This is a fruitless task unless one draws attention to Equation \ref{c} which reminds us that the product \(\mathrm{T} \, \mathrm{dS}\) is in fact a thermal energy. Chemists are familiar with spontaneous chemical reactions and Equations \ref{a} and \ref{b} present no conceptual problems [1].
Footnotes
[1] Robert Park, Voodoo Science, Oxford,2000. From page 7; ‘The first law says you can’t win; the second law says you can’t even break even’. This comment is with respect to fraudulent claims of discoveries of perpetual motion machines.