Problem Nr$.4(50$ points$)$

We consider arigid $($constant volume$)$ vessel of volume $\backslash (\backslash$mathrm$\{$V$\}=\backslash$mathbf$\{0.10\}\backslash$mathrm$\{$m$\}^\{3\}\backslash )($Pigure $3).$ The vessel contains initially wet steam of water $($mixture of saturated liquid water and saturated vapor$)-$ state $(1).$ At state $(1),$ the temperature of water is $\backslash (\backslash$mathrm$\{$T$\}\_\{1\}=100\{\}^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash )$ and the quality of steam is $\backslash (\backslash$mathbf$\{$X$\}\_\{1\}=\backslash$mathbf$\{0.15\}\backslash ).$ Subsequently, the wet steam undergoes heating to a final state $-$ state $(2).$ State $(2)$ is also in the wet steam region, and the corresponding temperature of wet steam is $\backslash (\backslash$mathrm$\{$T$\}\_\{2\}=145^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$

$($i$)$ Sketch the process $(1)-(2)$ in a p$-$v $($pressure $-$ specific volume$)$ chart. $(8$ points$)$

$($ii$)$ Using the data for state $(1),$ calculate the corresponding value of the mixture specific volume, $\backslash (\backslash$mathbf$\{$v$\}\_\{1.\}\backslash )(8$ points$)$

$($iii$)$ Calculate the total mass of water, $\backslash ($ m $\backslash ),$ within the vessel. $(6$ points$)$

$($v$)$ Determine the pressure of the mixture at state $(2),$ p$2.(6$ points$)$

$($vi$)$ Calculate the quality of steam at state $(2),\backslash (\backslash$mathbf$\{$X$\}\_\{2\}\backslash ).(10$ points$)$

$($vi$)$ Calculate the tatall $,$ the water mass, $\backslash ($ Q$\_\{1,2\}\backslash ).(12$ points$)$

Space provided for Ouestion $($i$)$

Answer: