B$.$ A well$-$insulated rigid tank having a volume of $0\mathrm{.}3m^3$ contains saturated water

vapor at a pressure of $1$ bar $($state $1).$ The water is rapidly stirred until the

temperature is raised at $T_2=500C($state $2).$ Then, insulation is removed

from the tank and the water is cooled at constant volume from $T_2=500C$ to

$T_3=360C($state $3).$ Do the following analysis:

$($a$)$ What property of the closed system is constant throughout the process

$($from state $1$ to state $2$ and finally to state $3)?$ What is the magnitude of

this property?

$($b$)$ Determine temperature and specific internal energy of water at state $1[2]$

$($c$)$ Determine state $2$ of water.

$($d$)$ Determine pressure and internal energy of water at state $2$ using

information from appropriate tables.

$($e$)$ Determine state $3$ of water.

$($f$)$ Determine pressure and internal energy of water at state $3$ using

information from appropriate tables.

$($g$)$ Sketch the two processes in series $($from state $1$ to state $2$ and from state

$2$ to state $3)$ on $p-v$ and $T-v$ coordinates.

$($h$)$ Formulate the $1^{st}$ Law of Thermodynamics for closed systems for the

process from state $1$ to state $2$ and calculate the work of the paddle wheel

in $kJ.$ Discuss the sign of the result.

$($i$)$ Formulate the $1^{st}$ Law of Thermodynamics for closed systems for the

process from state $2$ to state $3$ and calculate the heat in $[k]$ that is