Editing Calorimetry (section)

===Cumulation of heating===

For a time-dependent process of heating of the calorimetric material, defined by a continuous joint progression <math>P(t_1,t_2)\ </math> of <math>V(t)\ </math> and <math>T(t)\ </math>, starting at time <math>t_1\ </math> and ending at time <math>t_2\ </math>, there can be calculated an accumulated quantity of heat delivered, <math>\Delta Q(P(t_1,t_2))\, </math> . This calculation is done by [[line integral|mathematical integration along the progression]] with respect to time. This is because increments of heat are 'additive'; but this does not mean that heat is a conservative quantity. The idea that heat was a conservative quantity was invented by [[Antoine Lavoisier|Lavoisier]], and is called the '[[caloric theory]]'; by the middle of the nineteenth century it was recognized as mistaken. Written with the symbol <math>\Delta\ </math>, the quantity <math>\Delta Q(P(t_1,t_2))\, </math> is not at all restricted to be an increment with very small values; this is in contrast with <math>\delta Q\ </math>.

One can write

:<math>\Delta Q(P(t_1,t_2))\ </math>

::<math>=\int_{P(t_1,t_2)} \dot Q(t)dt</math>

::<math>=\int_{P(t_1,t_2)} C^{(V)}_T(V,T)\, \dot V(t)\, dt\,+\,\int_{P(t_1,t_2)}C^{(T)}_V(V,T)\,\dot T(t)\,dt </math>.

This expression uses quantities such as <math>\dot Q(t)\ </math> which are defined in the section below headed 'Mathematical aspects of the above rules'.