Problem $08\mathrm{.}096-$ Amount of ice added and entropy in insulated piston$-$cylinder device

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An insulated piston$-$cylinder device initially contains $0\mathrm{.}01$m$30\mathrm{.}01$m$3$ of saturated liquid$-$vapor mixture of water with a quality of $0\mathrm{.}1$ at $100$C$.$ Now some ice at $18$C is dropped into the cylinder. If the cylinder contains saturated liquid at $100$C when thermal equilibrium is established, the specific heat of ice at about $0$C is c $=2\mathrm{.}11$ kJ$/$kg$$C$.$The melting temperature and the heat of fusion of ice at $1$ atm are $0$Cand $333\mathrm{.}7$ kJ$/$kg$.$ Use data from tables.

The ice cubes at the bottom of the cylinder are labeled minus $18$ degree Celsius.

Problem $08\mathrm{.}096.$a $-$ Water vapor cooled by ice in a piston$-$cylinder device

Determine the amount of ice added.

The amount of ice added is g$.$