138 Physical Properties [CH. vi 



In the special case of hydrogen it is found that the ratio of the increase 

 of temperature to that of pressure is very approximately independent of the 

 volume. In other words, the value of a is extremely small for hydrogen. 

 For this reason the Comite Internationale des poids et mesures decided on the 

 constant- volume hydrogen thermometer as standard thermometer. The 

 small value which can be found for a is recognised in the stipulation of the 

 committee that the volume at which the gas is used is to be such that the 

 pressure at the melting-point of ice is to be the weight of 1000 mm. of 

 mercury at Paris. On this thermometer the readings are proportional to the 

 pressure above that at the melting-point of ice. If 6 is the observed tem- 



perature, we have 



T=T + a6, 



where a is a constant and T is the value of T corresponding to the melting- 

 point of ice. The relation between the two scales may obviously also be 



written 



T=a(0 + 0) .............................. (322). 



If the thermometer scale is to be the Centigrade scale, the values of a 

 must be such that at the boiling-point of water 6 = 100. On this scale it is 

 found that the point T = is given by 



6 =-# = - 273-04 C ......................... (323). 



This temperature is what is known as the absolute zero of temperature. 

 It is the temperature at which matter is entirely devoid of internal motion. 



If in equation (321) we take the temperature T to be that of the melting- 

 point of ice, and reduce the whole equation to the Centigrade scale, we put 

 (equation (322)) T = a0 Q , T l T Q = a6, and the equation becomes 



(P 1 -P.)0 0=l a 

 p0 Ptf 



The quantity *= ~- is what is usually known as the "pressure coefficient," 

 so that if we denote it by K P , the pressure at any temperature 6 is given by 



p 1 =p (l + K p 0). 

 Equation (316) now becomes 



_ 



This equation depends on the density but not on the temperature ; hence 

 for a given density, the pressure coefficient is independent of the temperature. 

 This law .was verified by Regnault*, who found that gas thermometers filled 

 with different gases gave identical readings over a great range of tempera- 

 ture. A single exception occurred in the case of sulphurous acid, of which 

 the anomalous behaviour appears to have been due to evaporation f. 



* Mem. de I'Acad. xxi. p. 180. 



t Van der Waals, Continuity, p. 392. 



