[helme]

The answer is 251C. But I couldn't get it.

[mjc123]

You need to know the temperature at which the saturated vapour pressure of water is 700 kPa. The question does not contain enough information to work this out if you don't know it or have access to tables. (Unless you have PVT data for steam, it also requires you to assume ideality, which is unlikely for saturated vapour, but then it does say "estimate", not "determine".)

[helme]

The specific volume of the vapor at 700kPa (164.97 C) is 0.2729 m^3/kg

On the other hand, I estimated the specific volume of the vapor at 700kPa (450 C) as 0.4834 m^3/kg

Then I found each of the masses by dividing 0.03 m^3 by their specific volumes. After that, I tried to continue with determining final specific volume by dividing 0.06 by the total mass. With the same logic, I determined final internal energy. But these values show me that the final temperature is 164 C at 700kPa by interpolation. Am I wrong with to assume that the final pressure would also be 700kPa? If so, what should I do?

[Enthalpy]

When you don't have steam tables, an approximation of the water liquid-vapour equilibrium is P(atm) = [0,01*T(°C)]⁴ between 1atm and a few 10atm. Tables are obviously better.

The question says "rigid tanks" so I feel no need to compute a final density. Each chamber keeps its volume and contents, heat just flows from one to the other, and the heat capacity at constant volume (or better, the tabulated internal heat) tells the final temperature. The only subtlety I see is that the masses differ, but you had already caught it.

As a quick check, I take a constant C_V (hence the same for both chambers) and get a final temperature of 268°C so 251°C might be possible with detailed data. On the other hand, 164°C isn't reasonable for being too close to one initial temperature and not even between both.

[helme]

Sorry. Not 164, it was 264.