A $0\mathrm{.}503$ kg sample is placed in a cooling apparatus that removes energy as heat at a constant rate. The figure gives the temperature $T$ of the sample versus time $t$; the horizontal scale is set by $t_s=176\mathrm{.}0$min. The sample freezes during the energy removal. The specific heat of the sample in its initial liquid phase is $3032\frac{J}{k}g-K.$ What are $($a$)$ the sample's heat of fusion and $($b$)$ its specific heat in the frozen phase?

$($a$)$ Number

Units

$($b$)$ Number

Units