Learning Goal:

Specifc heat, latent heat $--$ Comprehensive Problem Solving

An foam cup with negligible mass contains liquid sweet water with a mass of $0\mathrm{.}200$ kg and a temperature of $77\mathrm{.}0$C $.$

Take the specific heat of liquid water $($and sweet water$)$ to be $4190$ J$/$kg$$K $,$ the specific heat of ice to be $2100$ J$/$kg$$K $,$ and the latent heat of fusion for water to be $3\mathrm{.}34105$ J$/$kg $.$

How much ice at a temperature of $-22\mathrm{.}0$C must be dropped into the sweet water so that the final temperature of the system will be $32\mathrm{.}0$C $?$