CA$-2$ Suppose you have $2\mathrm{.}00$ kg of liquid water at a temperature of $20\mathrm{.}0$C$.$ You also have a large supply of ice cubes which are stored at a temperature of $20\mathrm{.}0$C$.$ The specific heat of solid ice is $2108$ J kg$1$C$1,$ the latent heat of fusion of water is $333,500$ J kg$1,$ and the specific heat of liquid water is $4186$ J kg$1$C$1.($a$)$ What is the maximum mass of ice you can mix with the liquid water so that all of the ice melts once thermal equilibrium is reached? Assume no heat is lost from the ice $+$ liquid water system during the process. $($b$)$ Suppose you add twice the mass of ice that you found in part a$.$ How much solid ice will remain once thermal equilibrium is reached? Hint: the final state will be a mixture of liquid water and solid ice.