We have produced some mathematical expressions, incorporating temperature and entropy, in order to describe quantitatively the effects of heat on the internal states of systems. But these are no use at all unless we can actually measure with some instrument the temperature or changes of entropy of a system. You may immediately think of the existence of thermometers. We say that these measure temperature. But how can they? Take as an example the familiar mercury-in-glass thermometer. The length of the mercury column (a thermometric property) varies with thermal intensity. So far, so good. But what do we know of the relation between that variation of length and thermal intensity? To begin with, we know nothing! Since we are ignorant of the relation between thermometric properties and thermal intensity, we have to define what it is we want to measure with no reference at all to thermometric properties. Having made this abstract definition, we have then to realize it in practice by using the thermometers. This is difficult, but not impossible with the science and techniques of thermodynamics.