thermodynamics - $ Delta H = C_p Delta T $

The definition of enthalpy as a function of heat capacity and temperature change. $ \Delta H = C_p \Delta T $.

Does it only apply at constant pressure? In my discussions on this board and also with links elsewhere, it looks like this equation applies during the Carnot Cycle, where there is no constant pressure.

Why is Cv used in the adiabatic expansion of Carnot Cycle to calculate internal energy

http://chemwiki.ucdavis.edu/Physical_Chemistry/Thermodynamics/Thermodynamic_Cycles/Carnot_Cycle

I generally think this equation does not need constant pressure to apply. However today, when I was going through Atkins Physical Chemistry, it specifically says:

$ \Delta H = C_p \Delta T $ (at constant pressure)

equation 2B.6b. I think the constant pressure part is wrong, but this is a book with 10 editions with 5 star reviews on amazon.

http://www.amazon.com/gp/product/1429290196/

Answer

Certainly, you agree $dH=C_P dT$ if we're at constant pressure. If $H$ and $C_P$ don't actually depend on pressure, then you can use this equation regardless of whether pressure changes. However, to determine $C_P$ and $H$ you first need an equation of state (such as $PV=NkT$). Without knowing the specific equation of state (aka, if your gas is ideal or not), you can only say $dH=C_P dT$ at constant pressure. However, in the specific case of the ideal gas, you know that both $H$ and $C_P$ don't depend on $P$, and so you can apply the equation more generally.