For a closed system doing reversible work of expansion the first law of
thermodynamics takes the form
dU = dQ - PdV /1/
where dU is the internal energy change, dQ is the heat absorbed, P is
pressure and V is volume. Since the system is CLOSED and undergoes
reversible changes the entropy change is, by definition, dS=dQ/T and
/1/ becomes:
dU = TdS - PdV /2/
J. Gibbs managed to convince the world that, if the system is OPEN
(substances are added to it), /2/ should be replaced by
dU = TdS - PdV + SUM mu_i dn_i /3/
where mu_i is the chemical potential and n_i is the amount of the ith
component. However Gibbs failed to explain the meaning of the entropy
change, dS, for an OPEN system. Was dS again equal to dQ/T, as for a
closed system, or was dS equal to something else when substances were
added to the system?
The fact that dS was not defined for open systems made the equation /3/
so fashionable (scientists adore equations with undefined terms) that
in the end /3/ was called "the fundamental equation of thermodynamics".
Yet scientists somehow felt that a new definition of dS would bring
even more money. The quickest among them, Ilya Prigogine, simply
combined /1/ and /3/ and obtained
dS = dQ/T - (1/T)SUM mu_i dn_i /4/
The Nobel Committee immediately gave him the money in the form of a
Nobel Prize.
Pentcho Valev
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