Thermo I Question: Two vessels coming to equilibrium. Finding final values.

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deltagal
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Hey, guys. I am currently in a Thermo I class and have ran into a problem that has me completely stumped. I have worked in numerous different ways and anything I come up with doesn't seem to make since or be realistic. Here's the question:

Two rigid vessels are connected by a small valve and tubing. Both are of negligible size. Vessel 1 contains .8m3 of water at 650kPa at a quality of 50%. Vessel 2 contains .4m3 of water at 400kPa and 250ºC. If the valve is oped and both vessels come to equilibrium, determine the final equilibrium pressure and the amount of heat transfer when the system reaches thermal equilibrium with he surroundings which are at 50˚C.

I have currently been using the continuity equations and using steam tables to get the values that I need. My Prof said I was on the right track but wasn't very helpful at all during our session. I hope you guys can give me some hints. Thanks.
 
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Step 1: Determine the total mass of water in the two tanks
Step 2: Determine the initial average specific volume = (total volume of tanks)/(total mass of water)
Step 3: Determine the initial internal energy in the two tanks
Step 4: Find the final state of the system for water at 50 C and the same average specific volume as initially to get the final pressure
Step 5: Determine the final internal energy
Step 6: Determine the change in internal energy
Step 7: The heat transfer is equal to the change in specific volume