amongst the Molecules of a Gas. 83 



against their mutual attractions. The two important general 

 results obtained were : — 



(1) The total cooling effect is directly proportional to the 

 difference of the pressures on the two sides of the plug. 



(2) The total cooling effect is inversely proportional to the 

 square of the absolute temperature of the gas. 



Although Thomson and Joule estimated the thermal 

 equivalent of pv — p'v' at 15°, they did not calculate its values 

 at different temperatures and subtract them from the total 

 cooling effect at the same temperatures, in order to get the 

 parts of the cooling effect at these temperatures due to increase 

 of the potential energy of the molecules. When this is done, 

 the cooling effect due to increased potential energy, which we 

 shall call 6, is, like the total cooling effect in (1), directly 

 proportional to the difference of the pressures on the two sides 

 of the plug, because at a given temperature pv — p'v 1 is very 

 nearly proportional top— p' . But (2) does not now hold for 

 6. In its place we have this result, that the cooling effect due 

 to increased potential energy is inversely proportional to the 

 absolute temperature : — 



In obtaining the values of pv — p l v r for air, Van der Waals's 

 formula was employed, 



(^ + "^^)(v-'0026) = l-0011(l+«0; 



the unit of pressure being that of a metre of mercury, and the 

 unit of volume that occupied by a kilogramme of gas at 0° C. 

 and a pressure of one metre of mercury ; a is the coefficient 

 of expansion, and t the temperature Centigrade. 



Thomson and Joule give the cooling effects at different 

 temperatures corresponding to difference of pressure of 100 

 inches, or 2*54 metres of mercury; so that to get values of 

 pv—p'v f corresponding to the same circumstances we must 

 put^> = *76 m., p'=3'S m. A kilogramme of gas is supposed 

 to pass through the plug. Changing to ordinary units and 

 dividing by the mechanical equivalent of heat J and the 



specific heat of air s, we get finally the cooling effects— — =Jt — y 



due to departure from Boyle's law, as tabulated below. 



The following table contains in the first column absolute 

 temperatures, in the second the actual total cooling effects at 

 the corresponding temperatures for a difference of pressure of 

 100 inches or 2'5 metres of mercury (these are taken from 



G2 



