Problem $4(30$ Points$)$ A sealed rigid cubical tank $111m$ contains a saturated mixture of water at $150C,x=0\mathrm{.}95.$ The tank is covered on all sides with a $100$ mm thick layer of polystyrene foam $(k=0\mathrm{.}035\frac{W}{m}K).$ It is placed in a $25C$ convective environment $(h=10\frac{W}{m^2})$ for $5$ hours. During the cooling transient the tank temperature remains at $150C.$ Find:

a$)$ The total amount of heat transferred. $(15$ points$)$

b$)$ The quality of the mixture at the final state. $(15$ points$)$

Ignore the thermal resistances of the tank wall and the internal convection.

Ignore radiation heat transfer.

Model the insulation as a one$-$dimensional plane wall.