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I have a question that bothers me. If we have a rigid container containing water at $P_1 = 1$ $atm$ and $T_1 = 25$ $°C$. If we add an electric resistance to heat the water inside, we go through heating of liquid and then boiling until we have the body filled with vapor. My question is how much if would take to reach the point where the vapor is saturated?

I have this in mind:

  1. For the heating of the liquid from $25$ to $100$ $C°$ at $1$ $atm$:

$m\displaystyle{ \times C_P \times \frac {dT}{dt} = Q_{heater}}$ (or is it $C_V$?)

So we get the time required to reach $100$ $°C$.

  1. For the vaporization, we know that the volume doesn't change, but the temperature and the pressure increase (which I can find if I look into the saturated vapor tables). So I was thinking about

$m \times h_{vap} = Q_{heater} \times dt$

This is the part that starts to become blurry in my mind. How can I calculate the time to evaporate all the liquid? It is obvious that the pressure of the vapor increases and that changes also the enthalpy of vaporization and the saturation temperature. Is there any way to account for this?

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  • $\begingroup$ Your comment on steam tables heads you in the right direction. You are basically calculating how much power is required to bring a boiler to operating pressure. So, yes, you have to account for the changing pressure in the boiler. $\endgroup$ – Jon Custer Apr 7 '16 at 13:40
  • $\begingroup$ Hey Jon, thank you for the reply. I have the power of the resistance. I just need to find the time to evaporate all the liquid. If I simply use the enthalpy of vaporization, the timing doesn't fit with my numerical calculations. I'm comparing analytical calculations with a model that I'm trying to develop. $\endgroup$ – Physther Apr 7 '16 at 13:57
  • $\begingroup$ As the pressure increases, so does the boiling point. You have to integrate over the steam tables appropriately for you situation (how much water, what is the volume, what is the energy input). $\endgroup$ – Jon Custer Apr 7 '16 at 14:02
  • $\begingroup$ Okay. So I can guess that one should use Antoine formula for the dependency of temperature and pressure. This would shift the boiling point. Or do you have any other suggestions on which equations should I use next? $\endgroup$ – Physther Apr 7 '16 at 14:48
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    $\begingroup$ Thank you @JonCuster and @Chester! After doing some analysis, I come to wonder... Do we really get vaporization in a rigid body filled up completely with water? If we would look on a P-v diagram, the pressure would increase isochorically and it would not reach the saturation conditions. Is this right or am I deviating from reality? As for your first question, Chester, I don't know how, but I can guess that there should be a way to split the system into liquid and vapor using the volume fraction. I don't know if I should invest time into this or if I can find some relations developed already. $\endgroup$ – Physther Apr 8 '16 at 9:23

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