Specific Heats for Non-Constant Processes Why can the specific heat at constant Pressure ($C_p$) be used to calculate the change in enthalpy as $\text{d}H = C_p\text{d}T\newcommand{\d}{\text{d}}$ for processes that are not even at constant pressure?
I have $\d H = C_p\d T + V\d p$. Why do we neglect the $V\d p$ term? For gases, $V$ the specific volume, can be very large, so an increase in pressure could have a non-negligible effect on the enthalpy. Is it so? Or not?
Cp of an ideal gas doesn't depend on pressure.  Cp of any substance is defined as the partial derivative of enthalpy respect to temperature at constant pressure.  But, if the enthalpy of the substance is independent of pressure, then it doesn't matter if the pressure is constant.  However, determining Cp by measuring the amount of heat required to change the temperature by a certain amount of the substance at constant pressure is still a standard method of measuring Cp.