Mixture of different gases at different temperatures

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Homework Statement


Hello. I have problém with this system. Mixture of two gases. How can i determine temperature T3?
Gas 1 (dry air) - I know T1, p1, m1
Gas 2 (water steam) - I know T2, p2, m2

Output (mixture) P3, (m1+m2); p3<p1;p3<p2

Homework Equations

The Attempt at a Solution


Is it possible to use this solution?
m1*c1*t1+m2*c2*t2=m1*c1'*t3+m2*c2'*t3
from the software tables
c1=function(p1;t1)
c1'=function(p3;t3)
c2=function(p2;t2)
c2'=function(p3;t3)​
?

Or i should use Daltons law to determine different partial pressure in c1' and c2'?

Excuse my English. I am working on it :)
 
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This is a process in the steam turbine seals. There is one "tube" with air, second "tube" with steam and they both point into the chamber. In chamber is vacuum (vacuum is made by vacuum-pump)
 
Sorry my mistake. p1=p2=p3 chamber is opened.