For Ag, $C_P\left({\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right)$ is given by 24 + 0.006 T/K. Calculate $\mathrm{\Delta }H$(in KJ) if 3 mole of silver are raised from 27° C to its melting point 927° C under 1 atm pressure.

$\begin{array}{r}{C}_p=(24+0.006\mathrm{T}){\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\\ T_1=300\mathrm{K}\\ T_2=1200\mathrm{K}\\ n=3\text{ moles }\\ p=1\text{ atm }\\ \end{array}$

$\mathrm{\Delta }H=3\times {\int }_{300}^{1200} (24+0.006T)dT=76950\mathrm{J}$

$\begin{array}{r}\mathrm{\Delta }H={\int }_{300}^{1200} 3(24+0.006T)dt\\ =3\left(24\right(1200-300\left)\right)+\frac{1}{2}0.006\left((1200{)}^2-(300{)}^2\right)\\ =76950\mathrm{J}=76.9\mathrm{kJ}\\ =77\mathrm{kJ}\end{array}$