THERMOMETRY.
For the first term we can substitute T1). We can obtain an expression for the second in terms of work against cohesion, of which in the van der Waals equation is a meas ure, so that If the units are litres, atmospheres, gram-moles and calories, the term within the bracket must be multiplied by 24.2, to convert litre-atmospheres into calories. We have then for oxygen and hydrogen the following values for the constants:— Considering the importance of the phenomenon, it is surprising that it has not received more attention. Such data as are avail able show that for expansion from pressures up to i oo atmos pheres to atmospheric pressure the cooling per one atmosphere difference of pressure increases almost linearly, for air, with de crease of temperature, and decreases with increase in temperature, as the simplified formula indicates. Putting k = o, the inversion temperature, above which the gas becomes heated on free ex pansion, and below which it is cooled, is found to be about 700° C for air and — 73° C for hydrogen, the latter value agreeing with Olszewski's experimental value —8o° C. Adopting the latter value for hydrogen, and the values —240-4° and —119.6° for the critical temperatures of hydrogen and oxygen, in accordance with the law of corresponding states, the inversion temperature for oxygen should be given by Experimental determinations of the mean cooling of air, when expanded, per atmosphere fall in pressure, seem, however, to indicate that the effect is not linear with the pressure difference, thus However, the measurements are difficult to make and the results are of doubtful value.
Cooling and Liquefaction by Free Expansion.—The sug gestion to utilise the Joule-Kelvin cooling effect for liquefying gases appears to have been first attempted independently by C. Linde in Germany and by W. Hampson in England. The first Linde plant was worked successfully in May 1895, and it produced several litres of liquid air per hour. This may be reckoned as the starting point from which important commer cial developments followed. Hampson's apparatus was first exhibited in England in March 1896. His process is the simpler; it is admirably suited for the production of liquid air in small quantity for experimental purposes ; and it has been very widely used in university and research institutions. The principle on which the apparatus works is as follows. Air compressed to about 200 atmospheres passes through a closely wound coil of copper pipe and expands at a valve at the lower end. Cooling takes place on expansion in accordance with the principle just discussed, and the cooled gas travels back through the interstices of the coiled pipe, cooling the compressed gas inside it. The coil acts
as a regenerator or heat exchanger, and the temperature of the air leaving the apparatus is only about a degree less than that of the air entering it. The cooling of the air being progressive, a steady state is reached when a part of the air escaping from the valves liquefies.
Hampson's Air Liquefier.—A section of the Hampson ap paratus is shown in fig. 11. The compressed gas enters at A and passes to the gauge, shown in elevation, through B to C, where the pipe forms four branches which are wound together to form the regenerator coil. The four pipes unite at D below the valve N, which is controlled by the spindle 00. The compressed air expanding at N is partially liquefied, the liquid collecting in E, and the vapour passing back between the coiled pipes of the re generator, and escaping through an outlet P. Liquid air is drawn off through the valve G, which is operated by F. The gauge H contains glycerol, and is connected below and above the level of the liquid in E by pipes K and M. The height to which the glycerol rises in M indicates the depth of the liquid in E. The efficiency of the process is of course dependent on the tem perature at which the air enters the coil, the pressures at the inlet and at the outlet and the mean value of k for the inlet tem perature, and the range of pres sure involved. In a well con structed apparatus the difference of temperature at the inlet and outlet is of the order of one de gree, and may be neglected. If the gas were simply allowed to expand without passing back through the coil, the fall in tern perature would be given by Cp X If the gas returned through the coil and n per cent of it liquefied the heat absorbed in the process would be (Cp t-I-X)n/ioo) when is the mean (molar) specific heat between the initial temperature and the boiling point of the gas, and X is the (molar) heat of evaporation. Equating these expressions in the case of oxygen compressed to 18o atmos pheres, the values of t being about 200° C For k=o-28 025 0-14 5.2 Bradly and Rowe (Phys. Review, 1904) found the yield of a Hampson liquefier to be 8.5% of the air passed through it, with out allowing for losses due to conduction of heat into the ap paratus, so that it would appear that the mean value of k does not fall off rapidly with increase in the pressure difference at the expansion valve.