Mr Searle, The Expansion of a Gas, etc. 243 



This equation, then, shows the fall of temperature t — t' due to the 

 expansion from v to v'. 



In the case of C0 2 , Van der Waals found 



(P + ^^K-OOO^ 1 ^, 



where P is the pressure in atmospheres, and V is the ratio of the 

 volume of 1 gramme to its volume (V Q ) at normal temperature 

 and pressure. Since one atmosphere is equivalent to 1014 x 10 6 

 dynes per square cm. and since V is 505 c.c, Van der Waals' 

 equation, when expressed in c.G.S. units, becomes 



V 0-00874 x 505 2 \ / v n ^ nn \ 1-00646, 



f 1Af + i UnF - 0-0023 = _,_- t, 



4 x 10 6 v 2 J Vo05 / 273 



f 2-26 x 10 9 \ 



I j?+ ? (^-116) = 1-89 xl0 6 £. 



U'014xl0 6 



_ 26 x 10 9 > 



1? ; 



Thus a = 2-26 x 10 !) cm. 5 grm. -1 sec." -2 . 



b = 1*16 c.c. per gramme. 



R = 1-89 x 10 K ergs per gramme per degree. 



According to Joly the mean specific heat at constant volume 

 over the range from about 15°C. to 100°C varies appreciably with 

 the pressure — an indication that Van der Waals' equation does 

 not completely represent the facts of the .case. For the present 

 purpose, however, G v may be taken as 017 x 42 x 10 7 or 7"14 x 10 6 

 ergs per gramme per degree. 



If in the expansion experiment the initial volume of 1 gramme 

 be 50 c.c. and the initial temperature 273°, the initial pressure 

 will be about 10 atmospheres. If the final volume be 100 c.c, we 

 have 



0-0« v 1 A9 / 1 "1 \ 



- JL =3-16°. 



, _ 2-26 x 10 9 f\_ _1_\ 

 7l4xl0 6 V50 100^ 



Thus, in the case of CO„, when the pressure falls from about 

 10 to about 5 atmospheres there is a cooling of about 3°C. 



By equating the energy of the whole of the gas in its final 

 state to the sum of the energies of the separate parts in their 

 initial states, it is easily shown that when two vessels of volumes 

 V x and V. 2 c.c. containing M x and M. 2 grammes of gas at tempera- 

 tures t x and t 2 are put into communication, the temperature t' 

 attained when thermal equilibrium has been established, is, for 

 small ranges of temperature, given by 



C v (M, + M,) t' = G v (MA + M. 2 t 2 ) - a l^- + -y-~ V y + y 



17—2 



