Enthalpy contribution and heat capacity

Imagine having at the input of a burner 105 mol/h of $\ce{O\_2}$ at 50 °C. The enthalpy contribution of this input mass is calculated using the Kirchhoff equation


$$\Delta H = \Delta H^° + \int\_{25 °C}^{50 °C} C\_p \,dT $$


where


$$ \Delta H^° = 0 \dfrac{\text{cal}}{\text{mol}}$$


$$C\_p = (7.129 + 0.1407 \cdot 10^{-2} \hspace{3pt} T - 0.6438 \cdot 10^{-5} \hspace{3pt} T^2) \dfrac{\text{cal}}{\text{mol} \cdot °\text{C}}$$


Compute the definite integral


$$ \int\_{25 °C}^{50 °C} C\_p \,dT = \Big( 7.129 \hspace{3pt} \Big[T\Big]^{50 °C}\_{25 °C} + 0.1407 \cdot 10^{-2} \hspace{3pt} \Big[\dfrac{T^2}{2}\Big]^{50 °C}\_{25 °C} - 0.6438 \cdot 10^{-5} \hspace{3pt} \Big[\dfrac{T^3}{3}\Big]^{50 °C}\_{25 °C} \Big) $$


The result will be a number whose unit of measure will be $\dfrac{\text{cal}}{\text{mol} \cdot °\text{C}}$. While enthalpy is measured in $\dfrac{\text{cal}}{\text{mol}}$, there is a discrepancy between the units of measurement.


Can you help me?


