Heat - Entropy

Entropy

In 1856, German physicist Rudolf Clausius defined the second fundamental theorem (the second law of thermodynamics) in the mechanical theory of heat (thermodynamics): "if two transformations which, without necessitating any other permanent change, can mutually replace one another, be called equivalent, then the generations of the quantity of heat Q from work at the temperature T, has the equivalence-value:"

In 1865, he came to define the entropy symbolized by S, such that, due to the supply of the amount of heat Q at temperature T the entropy of the system is increased by

and thus, for small changes, quantities of heat δQ (an inexact differential) are defined as quantities of TdS, with dS an exact differential:

This equality is only valid for a closed system and if no irreversible processes take place inside the system while the heat δQ is applied. If, in contrast, irreversible processes are involved, e.g. some sort of friction, then there is entropy production and, instead of the above equation, one has

This is the second law of thermodynamics for closed systems.