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

An insulated piston$-$cylinder device initially contains $0\mathrm{.}05m^3$ of saturated liquid$-$vapor mixture of water with a quality of $0\mathrm{.}1$ at $100C.$ Now some ice at $-18C$ is dropped into the cylinder. If the cylinder contains saturated liquid at $100C$ when thermal equilibrium is established, the specific heat of ice at about $0C$ is $c=2\mathrm{.}11k\frac{J}{k}g*C.$ The melting temperature and the heat of fusion of ice at $1$ atm are $0C$ and $333\mathrm{.}7k\frac{J}{k}g.$ Use data from tables.

Problem $08\mathrm{.}096.$b $-$ Energy saving through a preheating heat exchanger

Determine the entropy generated during this process. $($Round the final answer to four decimal places.$)$

The entropy generated during the process is $k\frac{J}{K}.$