The essential postulates of classical thermodynamics are formulated, from
which the second law is deduced as the principle of increase of entropy in
irreversible adiabatic processes that take one equilibrium state to another.
The entropy constructed here is defined only for equilibrium states and no
attempt is made to define it otherwise. Statistical mechanics does not enter
these considerations. One of the main concepts that makes everything work is
the comparison principle (which, in essence, states that given any two states
of the same chemical composition at least one is adiabatically accessible from
the other) and we show that it can be derived from some assumptions about the
pressure and thermal equilibrium. Temperature is derived from entropy, but at
the start not even the concept of `hotness' is assumed. Our formulation offers
a certain clarity and rigor that goes beyond most textbook discussions of the
second law.