What physical event did Clausius discover when he wrote his mathematical expression for thermodynamic entropy? The question has never been answered. It and other crucial knowledge is missing from fundamental physics. The root cause is due to this indispensable physics lesson being no longer taught , I quote from: 聽聽
College Physics; Sears, Zemansky; 3rd ed.; 1960; Page 1, Chapter 1:
"1-1 The fundamental indefinables of mechanics. Physics has been called the science of measurement. To quote from Lord Kelvin (1824-1907), "I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of Science, whatever the matter may be."
A definition of a quantity in physics must provide a set of rules for calculating it in terms of other quantities that can be measured. 聽Thus, when momentum is defined as the product of "mass" and "velocity," the rule for calculating momentum is contained within the 聽definition, and all that is necessary is to know how to measure mass and velocity. The definition of velocity is given in terms of length and time, but there are no simpler or more fundamental quantities in terms of which length and time may be 聽expressed. Length and time are two of the indefinables of mechanics. It has been found possible to express all the quantities of mechanics in terms of only three indefinables. The third may be taken to be "mass" or "force" with equal justification. We shall choose mass as the third indefinable of mechanics.聽
In geometry, the fundamental indefinable is the "point." The geometer asks his disciple to build any picture of a point in his mind, provided the picture is consistent with what the geometer says about the point. In physics, the situation is not so subtle. Physicists from all over the world have international committees at whose meetings the rules of measurement of the indefinables are adopted. The rule for measuring an indefinable takes the place of a definition. ...
Chapter 15, page 286; 15-1:
To describe the equilibrium states of mechanical systems, as well as to study and predict the motions of rigid bodies and fluids, only three fundamental indefinables were needed: length, mass, and time. Every other physical quantity of importance in mechanics could be expressed in terms of these three indefinables., We come now, however, to a series of phenomena, called thermal effects or heat phenomena, which involve aspects that are essentially nonmechanical and which require for their description a fourth fundamental indefinable, the temperature. ..."
What physical event did Clausius discover when he wrote his mathematical expression for thermodynamic entropy? - ResearchGate. Available from: https://www.researchgate.net/post/What_physical_event_did_Clausius_discover_when_he_wrote_his_mathematical_expression_for_thermodynamic_entropy [accessed Aug 14, 2016].