ABSTRACT
This is true for any complete reversible cycle. If now we proceed to the limit of infinitesimally small divisions of the path into adiabatic and isothermal steps, we may write
f aq 0 -= T (20) where the integration is carried over the complete reversible cycle. This is Clausius’ theorem; it was enunciated by him in 1854.‘*
If we now define a quantity S, the entropy, such that dS = aq,,,/T (bq,,, means an infinitesimally small amount of heat entering or leaving the system reversibly) we see that $dS = 0. In words: a small change in entropy dS is defined as equal to the small quantity of heat entering or leaving the body reversibly divided by the absolute temperature of the body. If heat enters the body its entropy increases and dS is positive; if heat leaves the body its entropy decreases and dS is negative.
