$${\left( {\frac{{\partial {\text{H}}}}{{\partial {\text{T}}}}} \right)_{\text{P}}}$$  is the mathematical expression for

Solution (By Examveda Team)

By the definition of $${C_P}$$ we can write $${C_P} = \mathop {\lim }\limits_{\delta T \to 0} {\left( {\frac{{\delta Q}}{{\delta T}}} \right)_P}.$$
Under constant pressure process and by first law of thermodynamics
$$\eqalign{ & Q = dH \cr & \Rightarrow {\left( {\frac{{\partial H}}{{\partial T}}} \right)_P} = {C_P}. \cr} $$