Editing Calorimetry (section)

==Special interest of calorimetry in thermodynamics: relations between classical calorimetric quantities==

===Relation of latent heat with respect to volume, and the equation of state===

The quantity <math>C^{(V)}_T(V,T)\ </math>, the latent heat with respect to volume, belongs to classical calorimetry. It accounts for the occurrence of energy transfer by work in a process in which heat is also transferred; the quantity, however, was considered before the relation between heat and work transfers was clarified by the invention of thermodynamics. In the light of thermodynamics, the classical calorimetric quantity is revealed as being tightly linked to the calorimetric material's equation of state <math>p=p(V,T)\ </math>. Provided that the temperature <math>T\, </math> is measured in the thermodynamic absolute scale, the relation is expressed in the formula

:<math>C^{(V)}_T(V,T)=T \left.\frac{\partial p}{\partial T}\right|_{(V,T)}\ </math>.<ref>{{harvnb|Truesdell|Bharatha|1977|p=150}}</ref>

===Difference of specific heats===

Advanced thermodynamics provides the relation

:<math>C_p(p,T)-C_V(V,T)=\left [p(V,T)\,+\,\left.\frac{\partial U}{\partial V}\right|_{(V,T)}\right ]\, \left.\frac{\partial V}{\partial T}\right|_{(p,T)}</math>.

From this, further mathematical and thermodynamic reasoning leads to another relation between classical calorimetric quantities. The difference of specific heats is given by

:<math>C_p(p,T)-C_V(V,T)=\frac{TV\,\beta _p^2(T,p)}{\kappa _T(T,p)}</math>.<ref name="LR 54"/><ref name="Kondepudi 181"/><ref>{{harvnb|Callen|1985|p=86}}</ref>