while working with a sample of a new $($totally real, definitely not made up$)$ chemical, Gregorian, you begin with a $0\mathrm{.}45$kg sample in it's solid state at $290$k$.$ The sample his placed in a sealed container and heated at a constant rate until it has completely melted into a liquid and has a temperature of $430$K$.$ Specific heat of gregorium $1800$ J$/$kg x k$.$ Specific heat of liquid gregorium $3300$ j$/$kg x k$.$ Heat of fusion of gregorium $4\mathrm{.}1$ x $10^5$ J$/$kg$.$ Melting$/$freezing point $380$K$.$ Heat of vaporization $6\mathrm{.}7$ x $10^5$ J$/$kg$.$ Boiling$/$condensation point of gregorium $510$K$.$

a$.)$ How much energy $($in the form of heat$)$ is added to your sample durning this process