300 HEAT. 



way, for the intrinsic energy corresponding to a given state is quite 

 independent of the manner in which that state is reached. Let A 

 (Fig. 170) represent the state of unit mass of the gas on the entrance 

 side, and B that of the same mass on the exit side of the plug. 



We shall suppose the change from A to B to take place along the 

 isothermal AC, and the equal pressure line CB, and to avoid consideration 

 of the variation of the different quantities, such as coefficient of expansion 

 and specific heat, we shall suppose A and B so near together that these 

 quantities are practically constant. 



The heat put in along AC is 



a0V(P -p) or atfVdP. 

 The heat put in along CB is K p dO 



where dO is the rise in temperature. The external work done is ACBNL. 

 Then e-E 



e - E = P V pv 



= AHOL-BKON 



aOVdP + Y. p dB = AHOL - BKON + ACBNL 

 = ACKH 



A l K dd m 



e =a-aV'dP <*> 



If dO = then 9 = - so that if a substance had the same temperature on 



a 



the two sides of the plug, equal expansions of that substance would 

 indicate equal intervals of temperature on the absolute scale. Hydrogen 



approaches 3 most nearly to this con- 

 dition, hence its use in the standard 

 gas thermometer. 



In their experiments Thomson 

 and Joule found that dd was propor- 

 tional to dP for a given temperature, 

 throughout the range of pressures 

 employed, and inversely as the 

 square of the absolute temperature, 

 so that we may put 



d6 A 02 



L * N dP~ H tf 2 



FIG. 170. where is the absolute tempera- 



ture of 0., II the atmospheric 



pressure, and A a constant for each gas, being the cooling per atmosphere 

 difference of pressure at C. 



The observed values for A were 



Air + '275 



Carbon dioxide .... +1*388 

 Hydrogen - 0'03 about 



