# Beta version

BETA TEST VERSION OF THIS ITEM

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

This online calculator is currently under heavy development. It may or it may NOT work correctly.

You CAN try to use it. You CAN even get the proper results.

However, please VERIFY all results on your own, as the level of completion of this item is NOT CONFIRMED.

Feel free to send any ideas and comments !

# Input data

Reference (known) boiling point | ||

Pressure for reference boiling point | ||

Enthalpy of vaporization of substance | ||

Substance | ||

Target pressure |

# Results

Boiling point under target pressure | 81.905732166 |

# 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:

$\dfrac{dp}{dT} = \dfrac{L}{T\Delta V}$where:

**$\dfrac{dp}{dT}$**- derivative of pressure after temperature under conditions of phase change equilibrium,

**$L$**- heat of phase transformation,

**$T$**- absolute temperature (in Kelvins),

**$\Delta V$**- 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):

$ln\left(\dfrac{p_2}{p_1}\right) = -\dfrac{\Delta H}{R}\left(\dfrac{1}{T_2} - \dfrac{1}{T_1}\right)$where:

**$p_1$**- pressure at state 1,

**$p_2$**- pressure at state 2,

**$T_1$**- boiling point at state 1 (under pressure $p_1$),

**$T_2$**- boiling point at state 2 (under pressure $p_2$),

**$R$**- gas constant,

**$\Delta H$**- enthalpy of evaporation of substance.

- Such an equation can be directly used to determine the boiling point under
**any pressure**:

$T = \left[\dfrac{1}{T_{ref}} - R \dfrac{ln \left(\frac{p}{p_{ref}}\right)}{\Delta H}\right]^{-1}$**$T_{ref}$**- known (reference) boiling point (under pressure $p_{ref}$),

**$p_{ref}$**- known (reference) pressure,

**$R$**- gas constant,

**$\Delta H$**- enthalpy of vaporization of substance,

**$p$**- the pressure for which we want to estimate the boiling point,

**$T$**- the boiling point under selected pressure.

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