HW #$3-4(20$ pt$)$ A mass of $3$ kg of saturated liquid$-$vapor mixture of water

is contained in a piston$-$cylinder device at $180$kPa.

Initially, $1kg$ of the water is in the liquid phase and the rest is in the vapor

phase. Heat is now transferred to the water, and the piston, which is resting

on a set of stops, starts moving when the pressure inside reaches $0\mathrm{.}6$ MPa $.$

Heat transfer continues until the total volume increases by $10$ percent.

Determine

$($a$)$ the initial temperature, quality, volume, and specific internal energy,

$,$ and $($:$u_1\}$

$($b$)$ the temperature, mass of liquid water, and specific internal energy $({}_{22}$

$m_{{?}_{?}}(1,2),$ and $u_2)$ when the piston first starts moving,

$($c$)$ the final temperature and specific internal energy $(T_3$ and $($:$u_3\}$

$($d$)$ the work done and heat transferred during this process $(W_{1-3}$&$Q_{1-3},(kJ))$

and $($e$)$ show the process on a $P-$v diagram.