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Say we have a cylinder of height $h_0$ and transversal area $S_\perp$ filled with water vapour and covered by diathermic walls, as well as a mobile diathermic piston on the top, which is in contact with a very big container which is at a temperature of $T_0$ and a pressure of $P_0$. Imagine we now place weights on top of the piston, and as soon as some water liquid appears, we stop putting weights. How we can try and find those masses?

I thought to try and start with the Clapeyron-Clausius, knowing that we know the $\Delta H_{vaporization}$ of the water and the molar mass $M$, we have that $$\frac{dp}{dT}=\frac{\Delta h}{T\Delta v}$$ being $p,v$ the molar volumes and molar pressures. I think we can also use the approximation in $\Delta v=v_{liquid}-v_{gas}\approx -v_{gas}$ but I'm pretty lost from here, since we don't know the final pressures or final temperatures either.

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  • $\begingroup$ Is the water vapor saturated in the initial condition? $\endgroup$
    – Chet Miller
    Commented Dec 6, 2023 at 11:56
  • $\begingroup$ @ChetMiller I don't know what you mean by saturated (I'm not native), in the initial condition, the only thing I know is that there is water in the vapour state inside the cylinder and after the compression, the first drop of water liquid appears. $\endgroup$
    – Ulshy
    Commented Dec 6, 2023 at 13:36
  • $\begingroup$ Do you know the definition of "specific volume." If so, do you know the specific volume of liquid water and water vapor at the temperature and pressure? $\endgroup$
    – Chet Miller
    Commented Dec 6, 2023 at 14:18
  • $\begingroup$ @ChetMiller understand now, sorry for the delay. No, the water vapour isn't saturated in the initial condition $\endgroup$
    – Ulshy
    Commented Dec 8, 2023 at 17:37
  • $\begingroup$ Then what is its temperature and pressure? $\endgroup$
    – Chet Miller
    Commented Dec 8, 2023 at 19:21

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