I am considering a liquid for which I know $C_p$ or $C_v$. I am wondering how this changes when you add a (minor) amount of solvent to the liquid. Is there a general theory around describing how a random liquid's heat capacity changes when you add a random solvent? Or is it a very specific process for the particular liquid and solvent one considers? References to literature would be very much appreciated!
If I understand You correctly, by solvent You mean any liquid different than Your 'main' liquid. If so, it is pretty straightforward, since it is a simple mixture of two liquids. If the heat capacity of main fluid is defined as 'energy required to change the temperature of a mass unit of an object by 1 K', then the heat capacity of the mixture is mass fraction-averaged:
$C_m$ = $g_1 * C_1 + g_2 * C_2$
If it is defined as 'energy required to change the temperature of one mole of an object by 1 K', i.e. it is molar heat capacity, then the molar heat capacity of the mixture is mole fraction-averaged:
$C_m$ = $x_1 * C_1 + x_2 * C_2$
$g$ and $x$ are mass and mole fractions of the components.