Problem $5(10$ points$)-$ Energy Balance and $P-v$ diagram

Two tanks $($tank A and tank B$)$ are separated by a partition. Initially tank A contains $1$ kg of steam at $1$ MPa

and $400C$ while tank B contains $4$ kg of saturated liquid$-$vapor mixture at $1\mathrm{.}5$ MPa with a quality of $0\mathrm{.}5.$

The partition is now removed and the two sides are allowed to mix until mechanical and thermal

equilibrium are established. If the pressure at the final state is $500$ kPa $,$ determine

A$.$ the temperature of the final state;

B$.$ the total internal energy of the final state;

C$.$ the amount of heat lost from the tanks;

D$.$ Sketch the state locations for both tanks on a P$-$v diagram. This sketch does not need to be

drawn to scale. The sketch should also include the $2-$phase dome and the isotherms curves

corresponding to initial and final states of both tanks.