ISOTHERMAL AND ADIABAT1C CHANGES. 299 



If it be not supplied, the air will cool by an amount nearly given by 



P p pv 1 

 p ' 2500 ' K^ 



where K^ is the mechanical value of the specific heat at constant 

 pressure. In fact the cooling will be rather less, because with lowering 

 of temperature the expansion against the atmospheric pressure is rather 

 less, pv is diminished, and therefore pv PV is less. 



In some of the experiments P was about 130 inches of mercury and 

 p was 30 inches. 



pv is about 780 x 10 6 in C.G.S. units, while K p is '2375 x 4'2 x 10 7 . 



Substituting these values in the expression for the cooling, we find 

 that it should be about 0'1 C. But the actually observed cooling was 

 about 0-9 0. Then some of the energy was also taken up in the 

 separation of the molecules, or there was an increase of intrinsic energy 

 on expansion. 



In a similar manner it may be shown that the cooling in the case of 

 carbon dioxide was chiefly due to change in intrinsic energy. 



In the case of hydrogen the product pv increases with the pressure. 

 Then, if the intrinsic energy is independent of the volume, energy must 

 be subtracted from the gas to keep the temperature the same in the 

 expanded condition. If it be not subtracted, the temperature will rise. 

 The actual effect observed was a slight heating, and of the order due to 

 the increase of pv. Hence it was concluded that the change in intrinsic 

 energy due to change in volume is very small. 



Use of the Porous Plug Experiment for the Comparison of the Air Scale 

 with the Absolute Scale. We may express the change in intrinsic energy 

 of the gas in two ways ; (1) in terms of the energy communicated from the 

 outside and (2) in terms of the observed changes of physical condition, 

 temperature, pressure, &c., and equating these two expressions we obtain 

 a. value for the absolute temperature. 



In considering the energy received from the outside, we remark that 

 on the whole there is very little change of temperature in passing through 

 the plug, though no doubt there are very great local variations in the 

 " rapids " the fine streams issuing from the pores. The gas is therefore 

 very nearly in temperature equilibrium with the surrounding walls and 

 the temperature slopes in these walls are very gradual. This is still 

 more nearly true since the gas was allowed to flow for so long a time 

 before observations were made that affairs had arrived at a steady state 

 and the wall at each point was at practically the same temperature as 

 the gas passing it. The walls were bad conductors so that the heat con- 

 ducted into or out of the gas might be neglected. The kinetic energy in 

 the gas was also small when it had settled down to steady motion beyond 

 the " rapids." Then the gain of intrinsic energy is practically due to the 

 difference between the works done on and by the gas on the two sides of 

 the plug or if E is the initial, and e the final, intrinsic energy, 



e - E = PY -pv. 



In finding the value of e E in terms of the observed changes in 

 physical condition, we may suppose the change made in any convenient 



