The specific heat capacity $c_p = c_p(T)$ (J/kg/K) of an ideal gas depends on its temperature.
However, the gas has a static temperature ($T_s$) and a total temperature ($T_i$).
As we have for the "sensible" enthalpy ($h$) and for the total enthalpy ($h_i$) :
$h = c_p*T_s$
$h_i = c_p*T_i$
what temperature ($T_s$ or $T_i$) should I use to calculate the $c_p$ of the gas ?
I am not sure of my logic, but I thought this : as the heat capacity $c_p$ measures how much we can raise the gas temperature ($T_s$ I supposed ?), and as the "sensible" enthalpy $h$ is the energy involved in the change of the gas static temperature, I consider that $c_p$ is calculated with the static temperature $T_s$, and not with the total temperature $T_i$
Thank you
Edit : in order to clarify what I mean by calculating $c_p$. For instance, let's say I have a gas surrounding an object, moving at a certain speed $V$ in the object reference, and I have the temperature-dependent equation of $c_p(T)$ of that gas (e.g, NASA polynomials). Because the gas is moving in the reference of the object, we define two temperatures : $T_s$ (static temperature) and (total temperature) $T_i = T_s + \frac{V^2}{2c_p} > T_s$ . I want to know if I have to calculate $c_p(T)$ with $Ts$ or $T_i$, both temperatures do not give the same $c_p$.