$(4$ points$)$

A large insulated bottle containing $764$ mL of water initially at $24\mathrm{.}9C$ is cooled by adding ice at $0C.$ Assume the specific heat of liquid water is constant at $4\mathrm{.}18\frac{kJ}{kgK}$ and the density of liquid water is

constant at $1000\frac{kg}{m^3}.$

Assume that the total energy of the water $+$ the ice does not change.

a$)$ If $51$ grams of ice is added to the bottle, what will the final temperature be$?$

$C$

b$)$ How much ice must be added if the desired temperatue is $8\mathrm{.}7C?$

g