Thermometry and the Temperature Concept

Practical measurements of temperature long preceded the theory of this important concept. Thermodynamics clearly requires the temperature concept, but thermometry (the theory of temperature measurements) is so deeply intertwined with general thermodynamic theory that we must take care to avoid logical circularity. 

Given this simple concept of thermal sameness or equilibrium, we can express the results of universal human observations in the following Inductive Law 3, also known as the zeroth law of thermodynamics  

Observation IL-3 Two bodies that are each in equilibrium with a third body are in equilibrium with one another. 

Observation IL-3 expresses the transitive nature of thermal equilibrium, i.e., that if A shares this property with B, and B shares it with C, then A also shares it with C. This observation may seem such an obvious aspect of experience as not to warrant special mention, but it guarantees that we can consistently speak of a definite property that is shared by all bodies in thermal equilibrium. We call this property temperature, denoted (provisionally) by the symbol . 

Let us first attempt to establish an operational mechanical temperature scale for that is based solely on mechanical concepts, such as pressure or volume, that are assumed to be well established. (Such a scale may be of little practical utility, but it satisfies the thermodynamicist s penchant for orderly logic.) To this end, we recall from IL-1 (Table 2.1) that only two properties suffice to uniquely fix the value of (as well as all other properties) of a simple gas. We may therefore choose P and V as these independent properties, and express by the functional relationship 

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Fahrenheit s and Amontons scales have a lot of common features with modern thermometric scales, which enabled the fundamental problems in scientific thermometry to be solved namely to assign a number 0, called the empirical temperature, to any given thermal state, to decide whether two bodies have the same temperature or not, and to determine which body has the higher temperature. Later Maxwell recognized that for thermometry to be a logically closed system it is necessary to add a concept of thermal equilibrium and another theorem, sometimes called the zero law of thermodynamics, according to which two bodies which are in thermal equilibrium with a third one are also in thermal equilibrium with each other. By establishing this theorem, which encompassed the form of Euclid s first axiom, the development of the concept of empirical temperature was practically completed. 

In general, to say that object A is hotter than object B is to say Ta > T. In this case, A will spontaneously transfer energy via heat to B. Likewise if B is hotter than A, Ta < Tb, and ener will transfer spontaneously from B to A. When there is no tendency to transfer ener via heat in either direction, A and B must have equal hotness and Ta = Tb- A logical extension of this concept says that if two bodies are at equal hotness to a third body, they must be at the same temperature themselves. This principle forms the basis for thermometry, where a judicious choice of the third body allows us to measure temperature. Any substance with a measurable property that changes as its temperature changes can then serve as a thermometer. For example, in the commonly used mercury in glass thermometer, the change in the volume of mercury is correlated to temperature. For more accurate measurements, the pressure exerted by a gas or the electric potential of junction between two different metals can be used. 

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