Entropy

Formulation and exploitation

Formulation

Rudolf Julius

Clausius

(1822-1888) has drawn conclusions from the following experience

Heat cannot pass by itself pass from a colder to a warmer body

or, in a later version

Heat cannot pass from a colder to a warmer body without compensation.

These are two formulations of the Second Law of thermodynamics.

We have already mentioned – as an assumption – that there are always positive

and

negative parts of the heat exchanged with a heat engine. Indeed, this is a consequence of the Second law. If it were different, we should be able to convert the heat of a part of the cold sea fully into work, and then convert the work back into heat by stirring a hot liquid. In this manner, in effect, heat would have passed from the cold sea to the hot liquid and this contradicts the Second Law. William

Thomson

(Lord

Kelvin

) has used this argument to express the Second Law in an alternative form,

viz

.

It is impossible to gain work in a heat engine by just cooling a body.

All of these statements are open to the criticism that they are verbally expressed and lack the stringency of mathematical formulae. It is a somewhat idle effort, however, to try and make these suggestive formulations strict, because in the end, when we have gone through

Clausius

’s argument, there is a mathematical formula, an inequality, and this is the proper mathematical form of the Second Law - and that

is

strict.