Isometric heat capacity

The first two are the conditions for thermal and mechanical stability derived in 8.1.2 the constraints on the isometric heat capacity (8.1.23) and isothermal compressibility (8.1.31) apply to mixtures as well as pure fluids. 

Response of IT, H, and S to changes in T. The response of the internal energy to an isometric change in T and that of the enthalpy to an isobaric change in T define the isometric and isobaric heat capacities,... 

These class II derivatives are extensive measurable state functions. Both and Cp are always positive, so U (H) always increases with isometric (isobaric) increases in T. The heat capacities are experimentally accessible by measuring the temperature change that accompanies addition of a small amount of energy (such as heat) to a system at constant volume, to yield C , or reversibly at constant pressure, to yield Cp that is. 

With the differential stability criteria (8.1.23) and (8.1.30) plus relations given in Chapter 3, we may identify bounds on other thermodynamic properties. For example, (3.3.31) relates the isometric and isobaric heat capacities. 

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