One winter evening you fill a pint$-$sized plastic cup with ice and water to drink before going to bed. The cup is $1/4$ ice and $3/4$ water all at $0$C

$.$ Use the densities of ice and liquid water to find the mass of each. You set the cup on the kitchen counter, forget about it$,$ and go to bed. The air in the kitchen is maintained at a constant $22\mathrm{.}2$C

by the central heating system of your apartment. When you wake up in the morning, the cup contains liquid water at $22\mathrm{.}2$C$.$

What is the entropy change of the ice water during the process in which it went from $0$C

to liquid water at $22\mathrm{.}2$C

as you slept?