The measurement of low temperatures is generally based upon observations of a gas thermometer, usually of the constant volume type, filled either with helium or with hydrogen at a pressure of i,000 mm. of mercury at the melting point of ice. The general theory of the instrument will be found in the article on THERMOMETRY. The correction of the observations to the absolute or Kelvin scale (see the JOULE-THOMSON EFFECT) is based upon the prin ciple that gases at very low pressures approach to the condition of the perfect gas, and the scale of the perfect gas thermometer is the nearest approach to realization of the absolute scale. A great deal of experimental work has been carried out, both by direct observation with gas thermometers filled at different pres sures, and by determining the compressibilities of the gases, and thereby determining the extent of the departure from the simple gas law, with a view to obtaining the values of important fixed thermometer points, such as the boiling and melting points of pure substances, on the absolute scale at high and low tempera tures. Observations of the vapour pressures of these substances can then be used instead of direct thermometric measurements. There is of course a practical limit to the use of a gas thermom eter, which is reached when the gas condenses and its vapour pressure falls below the smallest value of the gas pressure in millimetres of mercury which it is possible to measure. Such a condition was reached in the investigation on the solidification of helium, when the vapour pressure of the helium fell to a small fraction of a millimetre. The method of estimating such low temperature will be referred to later.
Temperature, Pressure and Volume Relationships.—The relationship of temperature, pressure and volume for important gases has been determined over a wide range of pressures and down to very low temperatures by workers in the Cryogenic laboratory, Leyden, and also in Berlin, and in Boston (Mass.) U.S.A. The method consists in compressing a known volume of gas into an apparatus similar to a gas thermometer, but much stouter, and measuring the pressure. When the pressure is large a considerable correction must be applied for the extension of the apparatus, and when the temperature of the bulb is far below that of the air, there is also a large correction for the volume of gas in the stem, and in the space above the mercury in the manometer. Owing to difficulty of estimating these corrections accurately the results obtained by different observers do not agree as closely as is desirable.
The volumes of saturated vapours and of the liquefied gases have been determined by a similar method, the liquid from a known volume of gas being condensed in a similar glass apparatus. However, since a space must remain between the surface of the liquid and the surface of the mercury In the manometer there is a liability for errors to creep in which increases as the critical temperature is approached, when the rate of change of volume with pressure is a maximum. The
data for the volume of liquid and saturated vapour and the critical volume, are the most dif ficult to obtain of all data relat ing to gas-liquid systems.
The de termination of the critical volume is made by taking advantage of a principle discovered by Cailletet and Matthias. On the left hand curve the points repre sent the volume of the saturated vapour, and those on the right hand curve the volume of the liquid for the same quantity of gas (one gram or one gram molecule), each pair of points repre senting one temperature. If now the distance between pairs of points be bisected the points of bisection lie on a line which is nearly or quite straight. The intersection of this line with the ordinate representing the critical temperature is the critical volume, the critical temperature being defined as the temperature at which liquid and vapour have the same density, or the same specific volume. The critical temperature is observed by corn pressing the gas in a glass tube as in the experiments of Andrews, and observing the appearance and disappearance of liquid as the temperature is allowed to fall and rise very slowly. The volume is varied slightly at the same time. The critical pressure, which is easiest to measure of all these constants, is observed when part of the compression tube is below the critical temperature and part is above it.
From the second law of thermodynamics it is easy to derive an equation, called the Clausius-Clapeyron equation, connecting the latent heat of vaporization LT at temperature T, dp with the slope of the vapour pressure curve and the change
dT of volume in passing from liquid (v) to vapour (V). Neglecting the volume of the liquid, and assuming that pV=RT we obtain and, on integration when K is a constant of integration.
It is possible to apply the first of these equations to calculate LT with some accuracy. Thus, in the case of nitrous oxide: Vapour pressure at 278° absolute . . . 40-21 atms.
„ „
,,
,,
atms. per
8,129.7 kg. per sq. metre per I°. Now at o° the mass of one cubic metre of the vapour is 8o kg. and that of the liquid is 903 kilograms so that if 422-4 is the mechanical equivalent of heat the experimental value being 59.5.
The most convenient experimental method for the determina tion of heats of vaporization is to pass an electric current through a thin wire immersed in the liquid, measuring the heat energy generated in the wire, and the quantity of the gas given off. How ever, the theoretical method yields results, which render experi mental work unnecessary in most cases. The data are of course of great value in the design of refrigerating machinery.