Measurable quantities in thermodynamics

The measurable quantities are mainly as follows heat capacities  

The present section is concerned mainly with the first two groups above, and in particular it will be shown how the various partial differential coefficients of the previous section may be expressed in terms of experimental magnitudes. 

The instantaneous heat capacity at the temperature T is the limiting value of this ratio as the quantities q and AT become infinitesimals  

There are several points to be noted about this ratio. In the first place C becomes infinitely large at points of phase change, for at such points heat is absorbed without giving rise to any change of temperature. For this reason the term heat capacity is usually applied only to changes of state not involving a phase change. 

Finally the value of C remains indefinite until the path of heating is specified. This may be seen by noting that, in the above expression for Cy the heat dg may be replaced by dU+dw, in accordance with the first law. However, the mere statement that there is a temperature change dT is insufficient to fix the values either of dU or of dw some other variable must be changed in a known manner, or held constant. It is therefore customary to define two particular kinds of heat capacity, Cy and C y which refer to constancy of volume and of pressure respectively. Thus 

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