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.