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Boiling point at any pressure calculator
Calculator finds out boiling point under selected pressure using Clausius-Clapeyron's equation and reference data for given substance. For example, you can find out what is water's boiling point in high mountains, where the pressure is lower.

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Reference (known) boiling point°C
Pressure for reference boiling pointhPa
Enthalpy of vaporization of substancekJ/mol
Substance
Target pressurehPa

Boiling point under target pressure81.905732166°C

Some facts

  • If we know the boiling point of the substance at some specific pressure (tables usually give the value under the so-called normal pressure i.e. 1013,25 hPa) and enthalpy of vaporization (molar heat of evaporation), then we can estimate the boiling point under another, selected pressure.
  • The relationship between pressure change and temperature change during evaporation (in general: phase transformation) is described by Clausius-Clapeyron equation. In the basic differential form, it looks as follows:
    dpdT=LTΔV\frac{dp}{dT} = \frac{L}{T\Delta V}
    where:
    • dpdT\frac{dp}{dT} - derivative of pressure after temperature under conditions of phase change equilibrium,
    • LL - heat of phase transformation,
    • TT - absolute temperature (in Kelvins),
    • ΔV\Delta V - change of volume accompanying the phase change.
  • In case of transformation of liquid into gas we can obtain the following relationship (after applying several approximations and integration):
    lnp2p1=ΔHR(1T21T1)ln\frac{p_2}{p_1} = -\frac{\Delta H}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)
    where:
    • p1p_1 - pressure at state 1,
    • p2p_2 - pressure at state 2,
    • T1T_1 - boiling point at state 1 (under pressure p1p_1),
    • T2T_2 - boiling point at state 2 (under pressure p2p_2),
    • RR - gas constant,
    • ΔH\Delta H - enthalpy of evaporation of substance.
  • Such an equation can be directly used to determine the boiling point under any pressure:
    T=[1TrefRlnpprefΔH]1T = \left[\frac{1}{T_{ref}} - R \frac{ln \frac{p}{p_{ref}}}{\Delta H}\right]^{-1}
    • TrefT_{ref} - known (reference) boiling point (under pressure prefp_{ref}),
    • prefp_{ref} - known (reference) pressure,
    • RR - gas constant,
    • ΔH\Delta H - enthalpy of vaporization of substance,
    • pp - the pressure for which we want to estimate the boiling point,
    • TT - the boiling point under selected pressure.


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