Calculating the boiling point of water

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  • #1
fluidistic
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Hi,
I'm looking through wikipedia for a formula to calculate the boiling point of liquids in function of the atmospheric pressure but I didn't find any.
In fact I'm curious what it would be for water on the Moon, Jupiter and so on.
By the way, is the fusion point pressure-dependent? I guess no.
So if a planet has a high pressure at ground level, I could heat up water and put a piece of iron and watching it being liquefied.
 

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  • #3
Mapes
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By the way, is the fusion point pressure-dependent? I guess no.

The melting temperature is indeed pressure-dependent, but the dependence is small compared to that of the boiling temperature. It's a function of the volume difference between the two phases, which is small and doesn't change much for solids and liquids.
 
  • #4
fluidistic
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Thank you very much to both.
The melting temperature is indeed pressure-dependent, but the dependence is small compared to that of the boiling temperature. It's a function of the volume difference between the two phases, which is small and doesn't change much for solids and liquids.
Do you have the formula?
 
  • #5
Mapes
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It's the same that mgb_phys mentioned, the Clausius-Clapeyron relation. For a phase change to occur (at constant temperature and pressure), the Gibbs free energies must be equal; i.e., [itex]\Delta G=0[/itex] when comparing the two phases. By definition, [itex]G=U+PV-TS[/itex], so [itex]\Delta G=\Delta U+P\Delta V-T\Delta S=0[/itex] and the change in phase change temperature for a given change in pressure is

[tex]\frac{\partial T}{\partial P}=\frac{\Delta V}{\Delta S}[/tex]

For small changes, we can assume that [itex]\Delta V[/itex] and [itex]\Delta s[/itex] are constant and use the fact that [itex]\Delta S_M=\Delta H_M/T_M[/itex] at the melting temperature ([itex]G=H-TS[/itex] by definition). [itex]\Delta H_M[/itex] is the easily found enthalpy of fusion. So we end up with

[tex]\Delta T_M\approx\frac{T_M\Delta V}{\Delta H_M}\Delta P[/tex]
 
  • #6
fluidistic
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Thanks mapes.
 

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