14 ATTAINMENT OF VERY LOW TEMPERATURES. 



accuracy of the results to within about two percent of the truth. The 

 final result leads to the conclusion that the theoretical quantity of liquid 

 air which it should be possible to obtain by the Hampson-Linde prin- 

 ciples, where the air is expanded from i8o atmospheres, is between 

 eight and nine percent of the air passing into the apparatus. 



The complete theoretical study of the Hampson-Linde process is 

 impossible, both on account of its highly complicated nature, and of our 

 ignorance of the thermodynamic properties of air over wide ranges 

 of temperature and pressure. The results stated above lead however 

 to conclusions which are interesting and are hardly likely to be merely 

 a matter of chance. 



If air were compressed to P atmospheres and allowed to expand, as 

 in the Hampson machine, but so that the current of air did not flow 

 back over the coil, the fall of temperature of the escaping gas at a short 

 distance from the jet could be calculated from the formula 



JT=y.{P-p), 

 and the heat absorbed by 



JQ = y.{P-p)Cp. 



where is the Joule-Thomson Effect and Cp is the specific heat at a 

 constant pressure of one atmosphere. 



Since the work done on the gas in bringing it toward the jet is 

 practically equal to the work done by the gas in its passage away from 

 the jet pv being very nearly constant, the quantity ^Q is a measure of 

 the change in the internal energy of the gas in passing from pressure 

 P to pressure p. This being the case it should be possible to pass over 

 intermediate stages to calculate the quantity of liquid air produced in 

 the Hampson apparatus from known data. 



The specific heat at a constant pressure of one atmosphere {Cp) has 

 been found by Witkowski* to have the value of 0.237 between 100° C. 

 and the temperature of liquid air ; the same value was obtained by 

 Regnault for the higher range of temperature. The Joule-Thomson 

 effect at 10°, the mean temperature of the air entering the liquefier, was 

 found by Joule and Lord Kelvin to be 0.25 °C. per atmosphere. The 

 latent heat of vaporization of air is about 50 cal. 



Suppose the air enters the. liquefier at 165 atmospheres pressure and 

 at 9.5°C. If i/x of the air liquefies at 87° abs.. 



Heat absorption on expansion = 0.25 X 0.237 X 164; 



Heat absorption due to cooling and liquefaction of x parts of air 

 = -'^ {50+ (0.237X206)}; 



Heat absorption due to cooling of unliquefied air ^ ( i — x) 

 (0.5 X -237). 



* Philosophical Magazine, July, 1896. 



