Mordechai L. Kremer Hebrew University Jerusalem, broel
I
I
The Ideal Car Eauation and Temperature Scale
In elementary treatments of thermodynamics both the concept of an ideal gas and the ideal gas temperature scale are introduced at an early stage. If one wishes to define the temperature scale with the aid of ideal gases, clearly one must define the ideal gas state without any reference to a temperature scale.' It will be shown that one can give a complete definition of the ideal gas state using an approximate temperature concept only. Th,e A p p r m i v ~ a t eDeJinilion of Temperature. Out of two bodies, that has the higher temperatnre which upon contact transmits heat to theother. As a consequence, two hodies have equal temperature, if they do not exchange heat upon eontact.
Definition of the Ideal Gas State. A gas is ideal, if during any infinitesimal change of pressure, volume and mass, the ratio pV/n remains constant, provided that, the temperalure does not change.
This last omdition is fulfilled, if the gas does not exchange heat with astandard hody in contact with it during any of these changes. It is a further characteristic of the ideal gas state that p V / n is a nionotonous function of T.
Whenever the temperature of the gas increases (determined by its relative ability to transfer heat to other bodies), p V / n increases too. The exact form of this monotonous function is not determined either by the approximate definition of temperature or by the definition of the ideal gas state. There is an infinite variety of monotonous functions consistent with both definitions. Each function gives a different definition of the temperature in terms of pV/n. We choose the simplest functional form, namely the proportionality, and define temperature qualitatively by f(Tj = KT' Vj where R is a yet undefined constant. We make our definition quantitative by giving R a certain value, like 0.082 liter atm/mole degree. In summary, our discussion shows that the equation (3)
pV = nRT
It contains the definition of ideal gas behavior (based on an approximate temperature concept) and the definition of a quantitative measure of temperature (based on the existence of ideal gases). is really a combination of two different equations.
Volume 43, Number 7 I , November 1966
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