From Section 2.4.1 of this link where the change in the specific internal energy of a gas is given as
$d u = \frac{\partial u}{\partial T} dT + \frac{\partial u}{\partial v} dv $
They define ideal gas as a gas where $\frac{\partial u}{\partial v} dv = 0 $ and define $C_v(T) = \frac{\partial u}{\partial T} $. I am wondering, for real gases, where $\frac{\partial u}{\partial v} dv $ is not zero, does the construction of $C_v(T)$ change (for example, is it still only a function of temperature even though the internal energy is not)? Or are the $C_v$ values in tables such as this valid for calculating the $\frac{\partial u}{\partial T} dT$ component of the $du$ equation for both ideal and real gases (even though the table specifies that it is for ideal gases)?
As a followup question, how are the tables of specific heats such as the one I linked above generated, is it from experiments or based off of theoretical calculations?