298 



HEAT. 



words, the internal or intrinsic energy is the same for the same temper- 

 ature whatever the volume. 



In such a case, therefore, Mayer's assumption would be justified. 

 But if, as was actually the case in Thomson's and Joule's experiments, 

 there is an alteration of temperature on the passage through 0, this 

 alteration may indicate either that Boyle's law is untrue or that Mayer's 

 assumption is untrue, or that both are untrue. We know already that 

 Boyle's law is only an approximation, and it remains therefore to de- 

 termine whether the alteration of temperature indicates that Mayer's 

 assumption is also only an approximation. 



In order to measure the change of temperature 

 accurately, Thomson and Joule forced the gas through a 

 porous plug consisting of a boxwood cylinder bb (Fig. 169), 

 1'5 in. internal diameter, containing two perforated brass 

 plates A, B, 2*72 in. apart, the space between these plates 

 being filled with cotton or silk, more or less compressed. 

 The gas was driven up to A through a long pipe immersed 

 in a constant-temperature bath, and flowed out from B 

 round a thermometer, being allowed there to come to the 

 atmospheric pressure. When a steady state of tempera- 

 ture was everywhere attained, there was with air a sensible 

 cooling, with carbon dioxide a much larger cooling, and 

 with hydrogen a very slight heating. 



Let us first investigate the effect which we might 

 expect if Boyle's law does not exactly express the relation 

 between volume and pressure, neglecting meanwhile the 

 effect of change in intrinsic energy. 



According to Amagat's researches, in the case of air 

 the product pv decreases by about 12 in 1000 for an 

 increase of pressure from 1 to 31 atmospheres. We are 

 perhaps not far wrong in assuming that the decrease is 

 nearly uniformly at the rate of 1/2500 per atmosphere 

 within these limits. With this assumption, if the air 

 is kept at the same temperature on the two sides of the 

 plug, and if ib expands to the atmospheric pressure p 

 on the further side, then 



B 



P Y 



FIG. 169. 



PV 



/, P-p 



=pv { 1 - 



\ p 



' 2500/ 



and 



or 



P - p t pv 

 ~~^T 2500 



pv exceeds PV by--~? . ~ 



And on the whole external work 



-- 

 2500 



is done by the air, and in 



order to keep the temperature constant this amount of energy must be 

 supplied from without. 



