Universal temperature scale

Two systems in thermal contact eventually arrive at a state of thermal equilibrium. Temperature, as a universal function of the state and the internal energy, uniquely defines the thermal equilibrium. If system 1 is in equilibrium with system 2, and if system 2 is in equilibrium with system 3, then system 1 is in equilibrium with system 3. This is called the zeroth law of thermodynamics and implies the construction of a universal temperature scale (stated first by Joseph Black in the eighteenth century, and named much later by Guggenheim). If a system is in thermal equilibrium, it is assumed that the energy is distributed uniquely over the volume. Once the energy of the system increases, the temperature of the system also increases (dU/dT> 0). 

A fundamental attribute of temperature is that for any body in a state of equilibrium the temperature may be expressed by a number on a temperature scale, defined without particular reference to that body. The applicability of a universal temperature scale to all physical bodies at equilibrium is a consequence of an empirical law (sometimes called the zeroth law of thermodynamics ), which states that if a body is in thermal equilibrium separately with each of two other bodies these two will be also in thermal equilibrium with each other. 

We have already shown that the absolute temperature is an integrating denominator for an ideal gas. Given the universality of T 9) that we have just established, we argue that this temperature scale can serve as the thermodynamic temperature scale for all systems, regardless of their microscopic condition. Therefore, we define T, the ideal gas temperature scale that we express in degrees absolute, to be equal to T 9), the thermodynamic temperature scale that we express in Kelvins. That this temperature scale, defined on the basis of the simplest of systems, should function equally well as an integrating denominator for the most complex of systems is a most remarkable occurrence. 

However, it is clear that slight variations in vessel shape, etched markings, or external pressure can lead to disagreements as to which thermometer gives the true temperature. Moreover, the reference points chosen to standardize the readings between different thermometers could be subject to disagreements (see Sidebar 2.4), as could the choice of thermometric fluid (e.g., Hg vs. water, each of which has different values of aP in different temperature ranges). Under these circumstances, the choice of the true temperature scale may become subject to non-scientific influences. We therefore seek a universal standard that avoids such arbitrary choices. 

Let us now describe the conditions of simplicity, universality, and minimal reference points that motivated adoption of the currently accepted international temperature scale. 

A rational temperature scale can be based on the limiting validity of the ideal gas equation of state (2.2) at sufficiently low pressure or density. This universal limiting behavior can be expressed in terms of the following Inductive Law 4 ... 

The ideal scale, as defined by (2.7a, b), also has an entirely different (and quite surprising ) theoretical basis, related to the maximum efficiency of machines and the second law of thermodynamics. This alternative definition of T(suggested by Kelvin) will be discussed in Section 4.5. However, we can recognize at this point that such a dual connection to fundamental thermodynamic principles of great universality gives (2.7a, b) a double-justification to be considered the true temperature scale. We henceforth adopt this definition of T throughout this book. 

Different empirical temperature scales will naturally differ from each other except at the respective fixed thermometnc points, Even different scales of the same type (say different Centigrade scales) will differ at all temperatures, except the steam point and ice point, depending on the fortuitous properties of the system chosen as a thermometer. It is, therefore, necessary to remove these differences and to obtain a more universal scale. This has been achieved in two ways. The practical way of achieving uniformity is to lay down detailed rules concerning the thermometer (actually different thermometers depending on the range of temperatures to be measured). Such rules have been agreed on internationally and... 

Inasmuch as the same function T of an empirical temperature scale serves as an integrating denominator of specific properties of the system under study, it is called the absolute temperature (function ) in thermodynamics and may be used as a universal function for measuring temperature. 

The time required for the synthesis of all elements in cosmic abundance also ranges from seconds to billions of years. The temperature scales fluctuate over several orders of magnitude (see Eigure 1). The chemical composition of the Universe, excepting the matter of neutron stars and black holes , can be presented as follows of 1,000,000 atoms there are 924,400 hydrogen, 74,000 helium, 830 oxygen. 

At the other side of the temperature scale, water has a most peculiar property it expands as it freezes, contrary to most known substances. Anyone who has suffered the misfortune of frozen water pipes in the winter will be all too familiar with this property. Were it not for this anomalous expansion, ice would sink when it freezes and form a frozen reservoir at the bottom of the oceans. Because of the low thermal conductivity of water, the oceans would not thaw out in the summer. Year after year the ice would increase in winter and persist through the summer, until eventually all or much of the body of water, according to the locality, would be turned to ice (Henderson, 1913, p. 109). Henderson further stated that [t]his unique property of water [the anomalous expansion on freezing] is the most familiar instance of striking natural fitness of the environment, although its importance has perhaps been overestimated but he added that on the basis of its thermal properties alone. . . water is the one fit substance for its place in the process of universal evolution, when we regard that process biocentrically (1913, p. 107). 

For the present we assume this low-density or ideal gas Kelvin (denoted by K) temperature scale is equivalent to an absolute universal thermodynamic temperature scale this is proven in Chapter 6,... 

National standard laboratories, such as the National Institute of Standards and Technology (NIST) in the United States, implement and maintain the practical temperature scale for their respective countries. They also help in the transfer of the scale by calibrating the defining standard thermometers These defining standard thermometers are costly to maintain and are primarily used in temperature calibration laboratories in industry or universities They are directly or indirectly used for calibration of thermometers used in actual applications. 

The choice of a temperature scale and the exact measurement of temperature are, in general, extremely difficult tasks. As yet, although much progress has been made, no scale for very low temperatures has been found to be universally acceptable. The situation for high temperatures is even worse since the problem of measurement of high temperatures has, at best, been only partially solved. It was pointed out above that the choice of a temperature scale is partly arbitrary. For convenience, a linear scale is usually employed. Use of a linear scale requires selection of an arbitrary zero and of an arbitrary scale unit. We shall discuss in detail the definitions of the centigrade, ideal gas, and absolute temperature scales. 

It is convenient to introduce the concepts of molecular weight and the universal gas constant at this point. We shall introduce these concepts by making use of Boyle s law and the absolute temperature scale. 

William Thomson, 1 Baron Kelvin of Largs, 1824—1907, Scottish engineer, mathematician, and physicist. Professor at the University of Glasgow, England. His major contributions to thermal analysis concern the development of the second law of thermodynamics, the absolute temperature scale (measured in kelvins) and the dynamic theory of heat. 

It is a very interesting coincidence that exactly at that temperature scale one expects the transformation of all elementary particles from massless quanta into the massive objects observed in today s experiments. The creation of the mass is due to the so-called Higgs effect. This consists of the condensation of an elementary scalar field (a close relativistic analogue of the Cooper-pairing in superconductivity). If this transformation had proceeded via a sufficiently strong first-order phase transition, the third of Sakharov s criteria had been also fulfilled by the behavior of the known elementary interactions in the very early Universe. 

The standard thermometers used are L N Model 8164 s that have been calibrated on the International Temperature Scale above 90 K and on the NBS Scale below 90°K at a total of 21 points. These calibrations were performed either at the Bureau of Standards in Washington or at the Pennsylvania State University. The modified Callendar equation was used to interpolate between the points on the International Temperature Scale and it is estimated that the accuracy of our curve is within 0.006 K. F or the points on the NBS Scale, it was found necessary to use two curves from 20° to 46°K, a log-log fit was made from 46° to 90°K, a semi-log fit was best. It is estimated that the maximum deviation of these two curves from the NBS Scale is 0.02°K. 

In 1845 Thomson was age 21. He had recently graduated from Cambridge University with high honors in mathematics, and was in Paris for discussions with French physicists and mathematicians. He had learned about Carnot s book from Clapeyron s 1834 paper but could not find a copy— no bookseller in Paris had even heard of it. Nevertheless, the information he had was sufficient for him to realize that Carnot s ideas would allow a thermodynamic temperature scale to be defined, one that does not depend on any particular gas. 

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