The entropy acts as a signpost of spontaneous change. (a) Entropy change is defined
in terms of heat transactions (the Clausius definition). (b) Absolute entropies are defined in terms
of the number of ways of achieving a configuration (the Boltzmann formula). (c) The Carnot cycle
is used to prove that entropy is a state function. (d) The efficiency of a heat engine is the basis
of the definition of the thermodynamic temperature scale and one realization, the Kelvin scale.
(e) The Clausius inequality is used to show that the entropy increases in a spontaneous change and
therefore that the Clausius definition is consistent with the Second Law.