the Constant-volume Gas-thermometer. 259 



we must have 



fa)- 



R 



\ 





tit 



X 



p= 



v-B v* 



The Difference between Joule 's Method and Lord Kelvin's 

 Method of Testing Mayer's Hypothesis. 



The formula obtained in the first section may also be 

 usefully employed to exhibit the precise connexion between 

 Joule's method and Lord Kelvin's method of testing Mayer's 

 hypothesis. The language of most text-books on this subject 

 is far from satisfactory; it is often implied that Lord Kelvin's 

 method is the same as Joule's except as regards delicacy; 

 and the relation between the two methods is never given 

 rigorously. 



Mayer's hypothesis consisted in assuming that for common 

 air and some other gases the amount of heat given out by the 

 gas during an isothermal compression was exactly equal to 

 the work done. Evidently, if this is so, there can be no change 

 of energy during an isothermal compression ; and we have 

 the energy remaining constant whenever the temperature 

 remains constant. This hypothesis was put to the test of 

 experiment by Joule, and roughly verified. Joule's apparatus 

 consisting of two large copper vessels is well known ; and it 

 is evident that his experiment tests Mayer's hypothesis directly. 

 For if the temperature remains unaltered, as Joule found to 

 be the case, the gas has received no heat and done no work, 

 so that it has not gained any energy from surrounding objects; 

 hence the constancy of temperature is accompanied by the 

 constancy of energy. 



The thermodynamics of Joule's experiment are easily given ; 

 we have in all cases 



dE = kdt+ \t(^-\-pl dv. 



Mtl-4 



(See ]*aynes's ' Thermodynamics,' p. 88.) Joule's result 

 shows that rfE and dt are zero simultaneously, while dv does 

 not vanish ; hence we obtain 



c 



£).-'-°- 



