980 
DR, J. JOLY ON THE SPECIFIC HEATS 
With regard to previous theoretical considerations, in reference to the temperature 
variation of the specific heat of a gas, it has been shown that where a gas departs 
from Boyle’s Law in the direction in which carbon dioxide does, there is reason to 
expect a diminishing specific heat with rise of temperature. This is based upon a 
thermodynamic equation due to Bankine.'"' 
Integrating tlie last and variable term in terms of the equation for an imperfect 
gas, 
PV = RT - a/TV, 
the value of K,, becomes 
K„ = C + 2a/TW, 
a being a constant. It follows that the specific heat at constant volume diminishes 
with rise of temperature till it attains to the limit C, which is designated by 
Clausius the true or real specific heat. From the second term, expressing the 
variable part, it is easy to calculate that at a density 0’124 the value of the variable 
term has the value 0‘0281 at 50° C., and 0’0223 at 90° C. in thermal units, a fall 
of 0’0058 thermal unit. Referring to the equation expressing the value of C„ iji 
terms of temperature derived from the experiments upon gas at this density, we find 
C„ at 50° = 0‘1971 and at 90° = 0'1894, or the fall has been 0'0077 thermal unit. 
The agreement is only approximate. However, the thermodynamic equation and the 
experiments agree in showing that the variation of specific heat with temperature at 
low densities is inappreciable ; thus the variable term at the density 0'00188 is almost 
inappreciable in value, and its changes, of course still more so. At 0° C. it has the 
value O'OOOT, at 50° C. the value 0’0004, and at 90° C. 0‘0003. 
Again, if we evaluate the variable term in the case of the density being O'OSOO— 
the second equi-density line on the plate—it is found that the sensibly rectilinear 
plotting of the experiments is in agreement with theory. The fall in the specific heat 
between about 10° and 100° C. calculates, in fact, to be 0'00103. This is a far wider 
range than the range of mean temperatures in the experiments. The experiments did 
not cover more than half this I’ange, and must have been competent to show a varia¬ 
tion of one part in 2000 upon values of (xr lying between 0‘223 and 0’054 grammes. 
This was hardly to have been expected. And this applies more forcibly to the lowest 
line, the density 0‘0456. 
On endeavouring to apply the thermodynamic equation to the line p = 0'180, it 
appeared that it was less agreeable with the experiments. The reason of this is 
probably to be found in the inapplicability of the formula to serve as the equation of 
the gas at high pressures. It is, in fact, based upon Regnault’s observations. Nor 
* ‘ TlTei'urodynamics,’ De Volson Wood, p. 118 
