which we call Heat. 125 
work, which as before I will denote by A. Let H be the quan- 
tity of heat thus determined. 
Further, let c be the specific heat of the gas under constant 
volume, in other words, the true specific heat ; then the increase 
of the quantity of heat in the quantity g of gas corresponding 
to an elevation of temperature dT is 
pee 
dH= n aT. 
Integrating this equation, we have 
Ss ig 
3 ee ak ect a Ee a) 
No constant need be added, since, as before remarked, the heat 
in the gas is proportional to the vis viva of the translatory mo- 
tion, and hence also to the absolute temperature. 
The expression on the right of this equation may be replaced 
by another which is very convenient for our present investigation. 
The quantity of heat which must be imparted to the quantity 
of gas qg in order to elevate its temperature by dT and its volume 
by dv is expressed thus, 
c 
i dT + pdv, 
wherein the first term represents the increase of the heat con- 
tained in the gas, and the second the quantity of heat consumed 
by work. If we assume the gas to be heated under constant 
pressure, the relation between dT and dv is thereby defined. For 
we have generally 
pv=T . const. ; 
and differentiating, under the supposition that p is constant, we 
obtain 
pdv=dT . const. ; 
whence the undetermined constant may be eliminated by means 
of the foregoing equation, and we have 
du= aT. 
Let us substitute this value of dv in the above equation, and at 
the same time note that, c! being the specific heat under constant 
pressure, the whole quantity of heat imparted to the gas in the 
case under consideration may be represented by dT. In this 
manner we arrive at the equation 
qe p96 gay PY 
RIT=% dT + T dT, 
