$(30$ points$)$ Numinum $(AI$ is melted at $661C.$ This melting process is considered as reversible process or equilibrium melting. During melting. $10700$ joules per mole of heat $($heat of fusion$)$ is absorbed$.$ Note that during melting, temperature and pressure $($I atm$)$ are constant. Atomic weight of $Al$ is $27g\frac{r}{m}ol.$

Calculate the heat required to rise the temperature of solid $1$kgAl from room temperature, melt it and hold it at $750C.$ The pressure is kept constant during heating and melting of $Al$ at $1$atm.

cpAl$(s)=20\mathrm{.}67+12\mathrm{.}38T,(\frac{\text{I}}{m}ol.K).,$cpAl$(I)=31\mathrm{.}76,(\frac{J}{m}ol.K)$