2 A. W. Witkowski on the 



thermodynamics. It follows that, in order to disclose the 

 whole of the calorimetric properties of a homogeneous fluid, 

 it is sufficient to investigate experimentally the specific heat, 

 in its dependence on temperature, under a single constant 

 pressure, together with its compressibility and thermal ex- 

 pansion. 



§ 2. Any state of thermodynamic equilibrium of the gas 

 may be defined by means of two independent variables, for 

 instance by its pressure p, and temperature 6 ( = t on the 

 absolute thermodynamic scale). Consider an infinitely small 

 change of state, corresponding to the increments dp and dt 

 of the variables ; then the gas does a quantity of work, 



dh =p^dt + p ^— dp ; 

 r d* dp r 



and absorbs a quantity of heat, 



dQ = mc p dt + l dp. 



We denote by m the mass of the fluid, by c p its specific heat 

 under the constant pressure p, by I a certain kind of latent 

 heat ; the last two quantities are to be considered as variables, 

 depending on p and t. 



The four coefficients ^-> ^ (thermal expansion and com- 

 pressibility), c p , and I, when known for every state (p, t) of 

 the body, give a full account of its thermodynamic properties. 

 They are not independent ; by the general laws of thermo- 

 dynamics they are subject to the relations 



/__i^ "dcp L^ m 



J dt > ^p - Jm dt 2 ' ' ' ' ' {L) 



where J denotes the dynamical equivalent of the heat-unit. 

 ^ Amongst other thermodynamic properties we have to con- 

 sider, in the first place, the specific heat at constant volume 

 = c v . It may be expressed in terms of the above coefficients 

 by the known equation 



or else by 



It follows from these equations, that the variations of the 



dv Jm ~dt 2 W 



