Specific Heats for Non-Constant Processes
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.