Question $1$

$($a$)$ A $\backslash (0\mathrm{.}2\backslash$mathrm$\{$~m$\}^\{3\}\backslash )$ tank initially contains water at $100$ kPa and a quality of $\backslash (1\backslash \%\backslash )($State $1).$ Heat is transferred to the water thereby raising its pressure to $2$ MPa $($State $2).$ At a pressure of $2$ MPa a safety valve opens and saturated vapor at $2$ MPa flows out. The process continues, maintaining $2$ MPa inside until the quality in the tank drops to $90\backslash \%($State $3).$ Determine:

$($i$)$ the mass of water at the initial state;

$($ii$)$ the temperature at State $2$;

$($iii$)$ the mass that flow out the tank;

$($iv$)$ the total heat transfer to the tank.

$(2$ marks$)$

$(2$ marks$)$

$(4$ marks$)$

$(6$ marks$)$

$($b$)$ A $\backslash (0\mathrm{.}5-\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ rigid tank A containing air at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $400$ kPa is connected by a valve to another $\backslash (0\mathrm{.}5-\backslash$mathrm$\{$m$\}^\{3\}\backslash )$ rigid tank B that holds air at $\backslash (50^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and $150$ kPa $.$ Now the valve is opened and the system is allowed to reach thermal equilibrium with the surroundings at $\backslash (15^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ Determine the mass of each tank and the final mixture pressure.

$(6$ marks$)$