# Is the specific heat capacity the same between real and ideal gases?

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?

If u=u(T,V) and $$C_V=\left(\frac{\partial u}{\partial T}\right)_V$$, then $$\left(\frac{\partial C_v}{\partial V}\right)_T=\frac{\partial^2 u}{\partial V\partial T}\neq 0$$So, for real gases, Cv can, in most cases, be expected to be a function of specific volume.