A $\backslash (0\mathrm{.}2\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ insulated tank A containing $3$ kg water at ambient temperature $\backslash (\backslash$left$(20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash$right$)\backslash )$ is connected by a valve to an uninsulated piston$-$cylinder device B that is initially evacuated $($i$.$e$.,\backslash (\backslash$mathrm$\{$m$\}\_\{\backslash$mathrm$\{$B$\}\}=0\backslash )$ at state $1).$ The tank contains an electrical resistance heater $($that is originally turned off$),$ and the mass of the piston is such that it requires a pressure of $1$ MPa to displace it$.$ The volume below the piston in cylinder B is $\backslash (0\mathrm{.}001\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ at the initial condition. With the valve closed, the electrical heater is turned on until all of the water in $\backslash ($ A $\backslash )$ has vaporized $($state $2-$ saturated vapor$).$ The valve is then opened, and steam is slowly allowed to flow until the pressure in A and B equalize, at which point the valve is closed $($state $3).$ During this

process, there is sufficient heat transfer between B and the environment to maintain the temperature inside B at ambient conditions. $($Helpful Hints: Assume the piston moves and assume reversible adiabatic expansion for A from State $2$ to $3)$

a$)$ Sketch the process path for Process $($Tank$)$ A ONLY on a T$-$s diagram with respect to saturation lines $(\backslash ($ F $\backslash )$ ifilio

Determine:

b$)$ the temperature $\backslash ((\backslash$mathrm$\{$K$\})\backslash )$ and pressure $\backslash ((\backslash$mathrm$\{$kPa$\})\backslash )$ in A at the end of the heating process,

c$)$ the mass transferred from A to $\backslash (\backslash$mathrm$\{$B$\}(\backslash$mathrm$\{$kg$\})\backslash ),$

d$)$ the work done on the piston $\backslash ((\backslash$mathrm$\{$kJ$\})\backslash ),$

e$)$ the heat transfer $\backslash ((\backslash$mathrm$\{$kJ$\})\backslash )$ from B $,$ and

f$)$ the entropy generated $\backslash ((\backslash$mathrm$\{$kJ$\}/\backslash$mathrm$\{$K$\})\backslash ).$