Thermometric scales

Let us consider unit mass of a fluid in a given state. Since the equations which we shall deduce in this paragraph do not depend on any particular thermometric scale, we shall represent the temperature by 6, where 6 may be the Centigrade temperature, or may be measured on any other temperature scale. The state of the fluid is therefore represented by (v, p, 6). If one of these variables increases by an infinitesimal amount there will, in general, be a corresponding increment in the value of each of the others, and there could be an infinite number of corresponding pairs of values of the latter for one value of the former. But if two variables are fixed, the state of the fluid is completely defined, for it has only two degrees of freedom ( 26). 

HYDROGEN SCALE. I, A thermometric scale. I See also Temperature Settles and Standards, i... 

When the temperature of pure ice is gradually raised under the ordinary atmospheric pressure, melting always commences sharply at a certain invariable temperature, which remains constant until fusion is complete. On account of the ease with which this constant temperature can be attained it has been chosen as the standard zero for the Celsius (Centigrade) and Reaumur thermometric scales. The melting-point is slightly affected by pressure, eaeh increase of one atmosphere lowering the transition temperature of ice to water by approximately 0-0075. 

Thermometer correction. The temperature which is read on the thermometric scale must be corrected because there are several errors in such determinations. One source of error arises from the construction and calibration of the thermometer. The bore of the capillary may not have the same diameter throughout further, the scale graduation and the calibration of low-priced thermometers are not very accurate. A second source of error is the method used in the common melting point apparatus. The common thermometer has been calibrated while totally immersed in a bath. In the melting-point apparatus described, only a part of the stem is immersed. The column of mercury above the oil bath has a lower temperature than that at which the thermometer was calibrated. Therefore either a thermometer calibrated by partial immersion should be used or a correction must be made for the unequal heating of the mercury in the stem of the thermometer. Although thermometers calibrated by partial immersion are available, the latter practice is the more common. 

Some investigators, Martine included, advocated the use of a thermometric scale based upon two fixed points. This had several great advantages. Any suitable liquid could then be used as... 

CELSIUS TEMPERATURE SCALE - A thermometric scale in which the freezing point of water is called 0°C and its boiling point 100°C at normal atmospheric pressure. 

Fahrenheit A thermometric scale in which 32 (IF) denotes freezing and 212 (IF) the boiling point of water under normal pressure at sea level (14.696 psi). 

I have repeatedly found that 1000 parts of common air of the temperature of 55° [F.] and common pressure, expand to 1321 parts in the manometer to which adding 4 parts for the corresponding expansion of glass, we have 325 parts increase upon 1000 from 55° to 212° or for 157° of the thermometric scale. ... 

Lord Kelvin, On an Absolute Thermometric Scale Founded on Carnot s Theory of the Motive Power of Heat, and Calculated from Regnault s Observations. Philos. Mag., 33, 313-317 (1848). Online at http //zapatopi.net/kelvin/papers/. 

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. 

W. Thompson On an Absolute Thermometric Scale founded on the Carnot s theory of heat motive power Phil. Mag. 33(1848)313... 

Why is the triple point of water (ice-liquid-vapor) a better fixed point for establishing a thermometric scale than either the melting point of ice or the boiling point of water ... 

Three different principles govern the design of bench-scale calorimetric units heat flow, heat balance, and power consumption. The RC1 [184], for example, is based on the heat-flow principle, by measuring the temperature difference between the reaction mixture and the heat transfer fluid in the reactor jacket. In order to determine the heat release rate, the heat transfer coefficient and area must be known. The Contalab [185], as originally marketed by Contraves, is based on the heat balance principle, by measuring the difference between the temperature of the heat transfer fluid at the jacket inlet and the outlet. Knowledge of the characteristics of the heat transfer fluid, such as mass flow rates and the specific heat, is required. ThermoMetric instruments, such as the CPA [188], are designed on the power compensation principle (i.e., the supply or removal of heat to or from the reactor vessel to maintain reactor contents at a prescribed temperature is measured). 

A comparison has been made between small scale test results and a field trial at a 17-ton scale for a solid compound [217]. The test results from a very sensitive calorimeter (Thermal Activity Monitor from ThermoMetric, Sweden) were substituted in a model, and the self-heating situation in bulk containers was predicted. The large-scale trial was carried out in a steel rectangular container lined with polyethylene. A control device was used to keep the container at a temperature of 40 to 45°C. Several thermocouples enabled monitoring of the temperature as a function of time in different places in the large container. 

As the magnirnde of the heat exchanged in an isothermal step of a Carnot cycle is proportional to a function of an empirical temperature scale, the magnitude of the heat exchanged can be used as a thermometric property. An important advantage of this approach is that the measurement is independent of the properties of any particular material, because the efficiency of a Carnot cycle is independent of the working substance in the engine. Thus we define a thermodynamic temperature scale (symbol T) such that... 

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. 

It is this remarkable property of gases that makes them valuable in thermometry, for the limiting values of (PV) are used to establish a temperature scale which is independent of the identity of the gas used as thermometric fluid. One need only fix the form of the functional relationship to T and define a... 

All thermometers, regardless of fluid, read the same at zero and 100 if they are calibrated by the method described, but at other points the readings do not usually correspond, because fluids vary in their expansion characteristics. An arbitrary choice could be made, and for many purposes this would be entirely satisfactory. However, as will be shown, the temperature scale of the SI system, with its kelvin unit, symbol K, is based on the ideal gas as thermometric fluid. Since the definition of this scale depends on the properties of gases, detailed discussion of it is delayed until Chap. 3. We note, however, that this is an absolute scale, and depends on the concept of a lower limit of temperature. 

Practical difficulties arise in making very precise determinations of temperature on the thermodynamic scale the precision of the more refined thermometric techniques considerably exceeds the accuracy with which the experimental thermometer scale may be related to the thermodynamic scale. For this reason, a scale known as the International Temperature Scale has been devised, with several fixed points and with interpolation formulas based on practical thermometers (e.g., the platinum resistance thermometer between 13.803 K and 1234.93 K). This scale is intended to correspond as closely as possible to the thermodynamic scale but to permit more precision in the measurement of temperatures. Further details about this scale are given in Chapter XVII. 

The establishment of the International Temperature Scale has required that the thermodynamic temperatures of the fixed points be determined with as much accuracy as possible. For this purpose a device was needed that measures essentially the thermodynamic temperature and does not depend on any particular thermometric substance. On the other... 

The simphcity of the relationship between the thermodynamic scale and the gas thermometer scale is due principally to the simple properties of rarefied gases, and also to the fortunate choice of mercury as thermometric substance by Celsius and Reaumur before the discovery of the gas laws. The coefficient of expansion of mercury happens to be almost exactly proportional to the coefficient of expansion of rarefied gases. All our thermodynamical relationships would have been very much more comphcated had water or alcohol, for example, or the resistance of a metal, been used for the definition of the practical scale of temperature. Their strict validity, however, would not have been affected. 

It follows, therefore, that when gases approximate to ideal behavior, i.e., at very low pressures, the differences in their thermometric properties disappear. This fact presents the possibility of devising a temperature scale which shall be independent of the thermometric substance, the latter being a hypothetical ideal gas. Such a scale is the so-called absolute ideal gas scale, in which the (absolute) temperature is taken as direcUy proportional to the volume of a definite mass of an ideal gas at constant pressure or to the pressure at constant volume. For convenience, the magnitude of the degree on the absolute scale is usually taken to be the same as on the centigrade scale ( 2b), so that the absolute temperature T on the ideal gas scale is given by... 

It will be seen in Chapter VII ( 18k) that it is possible to develop an absolute temperature scale, also independent of the nature of the thermometric substance, based on the second law of thermodynamics. This is sometimes called the Kelvin scale, in honor of its originator. Lord Kelvin (William Thomson). Actually, the thermodynamic scale can be shown to be identical with the absolute ideal gas scale, as defined above hence, temperatures on the latter, as well as the former, scale are represented by the symbol K. The ice point is consequently 273.16 K. It may be noted, incidentally, that the thermodynamic derivation of the absolute temperature scale provides a more definite interpretation of the absolute zero, i.e., the lowest limit of temperature, than is possible by means of the ideal gas thermometer. ... 

The air in Galileo s device was the thermometric substance, and its expansion or contraction depended upon changes in atmospheric pressure as well as temperature. Because of this, it is more properly called a barothermoscope, although its dependence on barometric fluctuations was not recognized until after the invention of the barometer in 1643 (Roller, 1960, pp. 12—13). Galileo also fitted his barothermoscope with a scale marking off degrees at pleasure, but he made no attempt to base the scale on standard temperatures that were reproducible. 

The third stage in the development of the modern thermometer began in 1665 with the development of the first thermometric standard scale. In that year Robert Boyle, Robert Hooke, and Christian Huygens suggested independently that thermometers could be calibrated effectively from a single fixed point. Degrees would represent a standard expansion or contraction fraction of the volume of the thermometric substance measured at the fixed point. Boyle set the fixed point at the freezing tempera-... 

The accuracy attainable with a liquid-in-glass thermometer is limited by the characteristics of the thermometer itself. Instability of the thermometric liquid, nonuniformity of capillary bore, and inaccuracies in scale graduation are the important factors. Uncertainties in corrections for the emergent stem may greatly limit the accuracy of partial-immersion thermometers. Generally, partial-immersion thermometers are assigned an uncertainty of 0.3°C in their calibration, whereas total immersion thermometers may have an uncertainty as small as 0.03°C. Observer errors add to the uncertainty but with care these can usually be made relatively small. 

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