Editing Calorimetry (section)

==Experimentally conveniently measured coefficients==

Empirically, it is convenient to measure properties of calorimetric materials under experimentally controlled conditions.

===Pressure increase at constant volume===

For measurements at experimentally controlled volume, one can use the assumption, stated above, that the pressure of the body of calorimetric material is can be expressed as a function of its volume and temperature.

For measurement at constant experimentally controlled volume, the isochoric coefficient of pressure rise with temperature, is defined by <ref name="IG 46">{{harvnb|Iribarne|Godson|1981|p=46}}</ref>

:<math>\alpha _V(V,T)\ = \frac{1}{p(V,T)}{\left.\cfrac{\partial p}{\partial V}\right|_{(V,T)}}  </math>

===Expansion at constant pressure===

For measurements at experimentally controlled pressure, it is assumed that the volume <math>V\ </math> of the body of calorimetric material can be expressed as a function <math>V(T,p)\ </math> of its temperature <math>T\ </math> and pressure <math>p\ </math>. This assumption is related to, but is not the same as, the above used assumption that the pressure of the body of calorimetric material is known as a function of its volume and temperature; anomalous behaviour of materials can affect this relation.

The quantity that is conveniently measured at constant experimentally controlled pressure, the isobar volume expansion coefficient, is defined by <ref name="IG 46"/><ref name="LR 54">{{harvnb|Lewis|Randall|1961|p=54}}</ref><ref name="Guggenheim 38">{{harvnb|Guggenheim|1967|p=38}}</ref><ref name="Callen 84">{{harvnb|Callen|1985|p=84}}</ref><ref name="Adkins 38">{{harvnb|Adkins|1975|p=38}}</ref><ref name="Bailyn 49">{{harvnb|Bailyn|1994|p=49}}</ref><ref name="Kondepudi 180">{{harvnb|Kondepudi|2008|p=180}}</ref>

:<math>\beta _p(T,p)\ = \frac{1}{V(T,p)}{\left.\cfrac{\partial V}{\partial T}\right|_{(T,p)}}   </math>

===Compressibility at constant temperature===

For measurements at experimentally controlled temperature, it is again assumed that the volume <math>V\ </math> of the body of calorimetric material can be expressed as a function <math>V(T,p)\ </math> of its temperature <math>T\ </math> and pressure <math>p\ </math>, with the same provisos as mentioned just above.

The quantity that is conveniently measured at constant experimentally controlled temperature, the isothermal compressibility, is defined by <ref name="LR 54"/><ref name="Guggenheim 38"/><ref name="Callen 84"/><ref name="Adkins 38"/><ref name="Bailyn 49"/><ref name="Kondepudi 180"/>

:<math>\kappa _T(T,p)\ = -\frac{1}{V(T,p)}{\left.\cfrac{\partial V}{\partial p}\right|_{(T,p)}} </math>