$(3)$ The temperature of $0\mathrm{.}200$ kg of liquid water is raised from $10\mathrm{.}0C$ to $100C$ and then converted to steam at $100\mathrm{.}0C$ by means of the apparatus shown in the figure. The lead shot maintains a constant pressure in the apparatus of $)=(3\mathrm{.}00$atm during the entire process. The volume of the $H_{2}O$ changes from $V_{\text{l}\text{i}\text{q}\text{u}\text{i}\text{d}}=0\mathrm{.}200{10}^{-3}{m}^3$ as the starting liquid to $V_{\text{g}\text{a}\text{s}}=0\mathrm{.}114m^3$ as the final gas. $\{$Density: ${}_{\text{w}\text{a}\text{t}\text{e}\text{r}}=1000k\frac{g}{m^3}$; specific heat: $c_{\text{w}\text{a}\text{t}\text{e}\text{r}}=4187\frac{J}{kgK}$&$,c_{\text{i}\text{c}\text{e}}=2220\frac{J}{kgK}$; Heats of transformation: $L_{\text{v}\text{a}\text{p}\text{o}\text{r}\text{i}\text{z}\text{a}\text{t}\text{i}\text{o}\text{n}}=2\mathrm{.}26{10}^6\{$:$\frac{J}{k}g,$&$,L_{\text{f}\text{u}\text{s}\text{i}\text{o}\text{n}}=3\mathrm{.}33{10}^5\frac{J}{k}g,\}$

a$)$ What is the work done by the $H_{2}O$ during the entire process?

b$)$ What energy is transferred between the $H_{2}O$ and the thermal reservoir as heat during the entire process? Is heat added or removed?

c$)$ What is the change in internal energy, $E_{\text{i}\text{n}\text{t}},$ of the $H_{2}O$ during this process?