$($b$)$ A vessel having a capacity of $0\mathrm{.}08m^3$ contains a mixture of saturated water and the saturated steam at a temperature of $250C.$ The mass of the liquid present is $11kg.$ Estimate the following properties of the mixture.

$($i$)$ The mass;

$[4]$

$($ii$)$ The dryness fraction;

$[3]$

$($iii$)$ The specific volume;

$[3]$

$($iv$)$ The specific enthalpy;

$[3]$

$($v$)$ The specific entropy;

$[3]$

$($vi$)$ The specific internal energy.

$[3]$

Take the steam properties at $250C$ are $p_{\text{s}\text{a}\text{t}}=36\mathrm{.}5$ bar, $v_f=0\mathrm{.}0001239\frac{m^3}{k}g,v_g=0\mathrm{.}0546\frac{m^3}{k}g,h_f=1061\mathrm{.}4k\frac{J}{k}g,h_{fg}=1740\mathrm{.}2k\frac{J}{k}g,S_f=2\mathrm{.}7474k\frac{J}{k}g,S_{fg}=3\mathrm{.}3585k\frac{J}{k}g.$