Hot water / cold steam interaction

[bamse207]

Hello,

I came to consider the following problem, and cannot seem to find the right way to tackle it.
It is not homework, merely a question I'd like to address out of personal curiosity:

Consider two volumes V1 and V2, each assumed adiabatic, and linked with a valve.
V1 is considered infinite (or at least very big compared to V2), V2 being finite and small compared to V1.
V1 is initially filled with, say, water, in liquid state at high pressure (T1, P1). T1 being below the saturation temperature at P1.
V2 is initially filled with steam at lower pressure and temperature (T2 < T1, P2 << P1)
At t=0, the valve is opened, what happens then?
According to the second principle, heat cannot be transferred from the cold steam to the hot water.
However it seems obvious to me that the end state would be liquid, at ~P1 and some other temperature.

Qualitatively, I'm expecting the liquid would flash through the valve from V1 to V2, which would gradually increase P2, until it equals P1. During that process, somehow, the steam in V2 would condense, increasing T2 upto a point where T2 > T1, from which heat can diffuse. Does this sound correct?

Any tips on the right approach to solving this? I've been through a couple of thermodynamics books, and couldn't find any mention of such a situation. Any pointers or keywords to look for to help me find an answer to such a case would be highly appreciated!

thanks!
Laurent
PS: this is my first post here, I hope I've found the right place for it...

 

[Jobrag]

I think that you have to give values to V1 and V2 then calculate the total mass and energy in V1 and V2 then combine them and see what temperature water you're left with.