KEVOS® MAKEOS · Engineering
Boiling Point Under Vacuum (Clausius–Clapeyron Boiling Temperature, Pressure for a Temperature Limit)
At what temperature will this liquid boil at the vacuum I can pull, and what pressure do I need to boil it below the highest temperature the product allows?
Boiling temperature of a liquid at a reduced (or raised) pressure from one known boiling point and the enthalpy of vaporisation, by the integrated Clausius–Clapeyron equation, and the absolute pressure at which it boils at the highest liquid temperature you allow, for vacuum drying, evaporation, distillation and degassing, against that temperature limit.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Known boiling temperature | °C | A boiling temperature of the liquid you know reliably, usually its normal boiling point. |
| Pressure at the known boiling point (absolute) | kPa | The absolute pressure that goes with that boiling temperature (101.325 kPa for a normal boiling point). |
| Molar enthalpy of vaporisation | kJ/mol | The molar enthalpy of vaporisation of the liquid, from a property table, near the temperatures of interest. |
| Operating pressure (absolute) | kPa | The absolute pressure in the vessel or dryer at the liquid surface. |
| Highest allowed liquid temperature | °C | The highest temperature the product or liquid may reach, from its stability, quality or safety limits. |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Known boiling temperature
- What it is
- A temperature at which the liquid is known to boil at a stated pressure, usually its normal boiling point at one standard atmosphere, used as the anchor point of the vapour pressure curve.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -270 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 100 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The calculated boiling temperature moves almost one for one with it.
- Get it right
- Choose a known point close to the conditions you are working at; the closer it is, the smaller the error.
What this means: Pressure at the known boiling point (absolute)
- What it is
- The absolute pressure that goes with the known boiling temperature, which is 101.325 kPa when that temperature is the normal boiling point.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0.000001 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 101.325 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher pressure for the same known temperature lowers the boiling temperature found at your operating pressure.
- Get it right
- Use absolute pressure; a gauge reading of zero is atmospheric, about 101 kPa absolute.
What this means: Molar enthalpy of vaporisation
- What it is
- The heat needed to evaporate one mole of the liquid at constant temperature, which sets how steeply its vapour pressure changes with temperature.
- Units and format
- Enter a number in kJ/mol: kJ/mol. The form accepts 0.1 kJ/mol to 1000 kJ/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 40.656 kJ/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger value means the boiling point changes less for a given change in pressure.
- Get it right
- Tables may give it in kJ/kg; multiply by the molar mass in kg/mol to get kJ/mol.
What this means: Operating pressure (absolute)
- What it is
- The absolute pressure above the liquid surface in the dryer, evaporator or vessel during operation.
- Units and format
- Enter a number in kPa: kilopascals. The form accepts 0.000001 kPa to 100000 kPa. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kPa as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A lower pressure lowers the boiling temperature.
- Get it right
- Measure it at the vessel; a gauge at the vacuum pump reads lower than the vessel because of line losses.
What this means: Highest allowed liquid temperature
- What it is
- The highest temperature the liquid or product may reach without damage, loss of quality or a safety problem, used as the pass or fail limit.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -270 °C to 2000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 65 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Only moves the pass or fail line and the pressure needed; the boiling temperature does not change.
- Get it right
- Take it from the product specification or stability data, not from the heating medium temperature.
Method and formulas
- Clausius–Clapeyron: ln(P ÷ P1) = −(ΔH_vap ÷ R)(1 ÷ T − 1 ÷ T1), with an ideal vapour, a negligible liquid volume and a constant ΔH_vap.
- Boiling temperature T = 1 ÷ (1 ÷ T1 − R ln(P ÷ P1) ÷ ΔH_vap); pressure at the limit P = P1 exp(−(ΔH_vap ÷ R)(1 ÷ T_max − 1 ÷ T1)).
- Example: water (100 °C at 101.325 kPa, 40.656 kJ/mol) boils at 58.886 °C at 20 kPa; it boils at 65 °C at 26.102 kPa.
Limitations
- ΔH_vap is taken as constant, so the error grows the further the result is from the known boiling point.
- Pure liquid at its free surface; dissolved solids raise the boiling point and liquid depth adds hydrostatic head.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the vacuum for drying or evaporating a heat-sensitive product
- Find the boiling point of a solvent at a vacuum pump’s pressure
- Check whether water will boil off in a vacuum degassing step
Who it is for
- Process and chemical engineers
- Vacuum equipment specialists
- Production engineers
What you get
- Boiling temperature at the operating pressure
- Shift from the known boiling point
- Absolute pressure needed to boil at the temperature limit
Interpreting the result
- Each halving of the absolute pressure lowers the boiling point by a step that shrinks a little as the temperature falls; per kilopascal, the deep end of the vacuum gains most.
- Below its freezing point a liquid freezes instead of boiling; the equation then describes sublimation only with the enthalpy of sublimation.
Before relying on the result
- Compare the result with measured vapour pressure data for the liquid when the shift is large.
- Measure the pressure at the vessel, not at the pump, because line losses raise it.
References
- Linder, B., Thermodynamics and Introductory Statistical Mechanics (Wiley-Interscience, 2004), sections 9.2–9.3, printed pp. 96–97: the Clapeyron equation and the integrated Clausius–Clapeyron equation. Method reference; no source text, tables or examples are reproduced.
Learn the Concepts Behind This Tool
These KEVOS® Library readings explain the method this tool uses, with worked examples.
Explains the concept · KEVOS® original book
Vapour, outgassing and gas loads
What it covers: Gas load once the air is gone: vapour pressure and Clausius–Clapeyron checked against NIST, evaporation limited by heat, resin and walls, and a wet container.
Method explained here · KEVOS® original book
Recovering solvent
In Solvent Vapours by the Numbers
What it covers: When condensing solvent from an air stream can and cannot work, the saturation limit on recovery, distilling dirty thinner under vacuum to keep it cool, and what a small still saves.
Useful alongside · KEVOS® original book
Liquefied gases, vapour pressure and the critical point
What it covers: Vapour pressure and Clausius–Clapeyron, liquid nitrogen in a microbulk tank, why warm liquid holds less, CO₂ cylinders that go liquid-full in summer, and a tank sized at the wrong density.
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