KEVOS® MAKEOS · Engineering
Boiling Point and Vapour Pressure at Operating Pressure (Clausius–Clapeyron Check)
At the pressure over my liquid (a vacuum, a tank at altitude or a pressurised vessel), at what temperature will it boil, what is its vapour pressure at my process temperature, and is there enough margin to keep it from boiling or flashing?
Boiling point and vapour pressure of a liquid away from a known point, by the integrated Clausius–Clapeyron equation (vapour treated as an ideal gas, latent heat taken as constant): from a known boiling point and its pressure, the latent heat of vaporisation and the molar mass, it gives the boiling temperature at the operating pressure, the vapour pressure at the liquid’s highest temperature, the margin between them against the margin you require, and how far the estimate is taken from its reference point.
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How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Known boiling point (reference) | °C | A boiling point you trust: the normal boiling point at 101.325 kPa from property data, or a measured point nearer the operating condition. |
| Pressure at the known boiling point | kPa abs | The absolute pressure that goes with that boiling point. |
| Latent heat of vaporisation | kJ/kg | Latent heat of vaporisation near the temperatures of interest, from property data (water 2257 kJ/kg at 100 °C, larger at lower temperatures). |
| Molar mass of the liquid | g/mol | Molar mass of the liquid (water 18.015 g/mol). |
| Process | ||
| Operating pressure over the liquid | kPa abs | Absolute pressure above the liquid surface: vacuum gauge reading in absolute terms, local atmospheric pressure or the vessel pressure. |
| Highest liquid temperature in the process | °C | Highest temperature the liquid reaches in the process, at the point where the pressure is lowest. |
| Required margin below boiling | K | How far below its boiling point you want the liquid to stay, to allow for measurement error, hot spots and the approximation. |
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 point (reference)
- What it is
- A boiling temperature of the liquid that you trust, the anchor point from which the vapour-pressure curve is drawn.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -270 °C to 1000 °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
- Moves the whole vapour-pressure curve; the boiling point at the operating pressure moves the same way, slightly less than one for one.
- Get it right
- The closer this point is to the operating pressure, the more accurate the estimate; a measured point near the operating condition beats the normal boiling point.
What this means: Pressure at the known boiling point
- What it is
- The absolute pressure that goes with the reference boiling point; for the normal boiling point it is one standard atmosphere.
- Units and format
- Enter a number in kPa abs: kPa abs. The form accepts 0.001 kPa abs to 100000 kPa abs. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 101.325 kPa abs as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A higher reference pressure for the same boiling point lowers the predicted boiling point at the operating pressure.
- Get it right
- Always an absolute pressure: never a gauge or vacuum reading.
What this means: Latent heat of vaporisation
- What it is
- The heat needed to turn one kilogram of the liquid into vapour at constant temperature; it sets how steeply the vapour pressure rises with temperature.
- Units and format
- Enter a number in kJ/kg: kJ/kg. The form accepts 1 kJ/kg to 100000 kJ/kg. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 2257 kJ/kg as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A larger latent heat makes the vapour pressure change faster with temperature, so the boiling point moves less for a change of pressure.
- Get it right
- Latent heat rises as the temperature falls; use a value near the temperatures you are working at.
What this means: Molar mass of the liquid
- What it is
- The mass of one mole of the liquid, which turns the latent heat per kilogram into the molar latent heat used in the Clausius–Clapeyron equation.
- Units and format
- Enter a number in g/mol: g/mol. The form accepts 1 g/mol to 2000 g/mol. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 18.015 g/mol as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Multiplies the latent heat in the same way, so it steepens the curve in proportion.
- Get it right
- For water use 18.015; for a mixture the method does not apply.
Process
What this means: Operating pressure over the liquid
- What it is
- The absolute pressure acting on the liquid surface in the process: the vessel pressure, the vacuum level or the local atmosphere.
- Units and format
- Enter a number in kPa abs: kPa abs. The form accepts 0.001 kPa abs to 100000 kPa abs. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 20 kPa abs as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- Lower pressure lowers the boiling point and so the margin.
- Get it right
- Convert a vacuum gauge reading to absolute pressure: atmospheric pressure less the vacuum shown.
What this means: Highest liquid temperature in the process
- What it is
- The hottest the liquid gets where the pressure is lowest, which is where boiling or flashing would start first.
- Units and format
- Enter a number in °C: degrees Celsius. The form accepts -200 °C to 1000 °C. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 50 °C as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- A hotter liquid raises its vapour pressure and cuts the margin one for one.
- Get it right
- Take the temperature at heating surfaces or the hottest point, not the average of a well-mixed tank.
What this means: Required margin below boiling
- What it is
- How far below its boiling point the liquid must stay, covering measurement error, hot spots and the approximation in the method.
- Units and format
- Enter a number in K: kelvin (a difference of 1 K equals 1 °C). The form accepts 0 K to 200 K. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 5 K as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The decision fails when the calculated margin is below this value.
- Get it right
- A few kelvin is common for process control; allow more where boiling would be dangerous or the estimate is far from its reference.
Method and formulas
- Clausius–Clapeyron with the vapour as an ideal gas and the liquid volume neglected: dp/dT = p ΔH ÷ (R T²) (Greiner eqs 3.13–3.14), with ΔH = L × M the molar latent heat.
- Integrated between the known point and the operating point (Greiner eq. 3.15): 1/T_b = 1/T₀ − (R ÷ ΔH) ln(p ÷ p₀) and p_v(T) = p₀ exp[−(ΔH ÷ R)(1/T − 1/T₀)].
- Margin = T_b − T_liquid; the slope of the vapour-pressure curve at the boiling point, p ΔH ÷ (R T_b²), shows how much the boiling point moves for a small pressure change.
- Example: at 20 kPa abs the liquid boils at 58.889 °C; at 50 °C its vapour pressure is 13.338 kPa abs, a margin of 8.8895 K.
Limitations
- Latent heat is taken as constant and the vapour as ideal, so the error grows with the distance from the reference point and near the critical point; for water the estimate from 100 °C runs about 1 K low at 20 kPa abs. Use steam tables (IAPWS-IF97) or measured vapour-pressure data where accuracy matters.
- Pure liquids only: dissolved solids raise and volatile components lower the boiling point, and mixtures boil over a range.
- The pressure is the pressure at the liquid surface; hydrostatic head raises the boiling point lower in a deep vessel.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Set the vacuum for drying, degassing or distillation without boiling the liquid
- Check that a hot liquid will not flash where the pressure drops
- Estimate the boiling point at a site’s lower atmospheric pressure
Who it is for
- Process and chemical engineers
- Maintenance engineers
- Laboratory and quality staff
What you get
- Boiling point at the operating pressure
- Vapour pressure at the liquid temperature
- Margin to boiling against the margin required
Interpreting the result
- Under vacuum the boiling point falls fast: halving the absolute pressure lowers it by tens of kelvin for water near room temperature, which is why vacuum drying works at low temperature.
- A margin of zero or less means the liquid boils or flashes at the stated conditions; small margins are easily lost to temperature errors or local hot spots.
References
- Greiner W., Neise L. and Stöcker H., Thermodynamics and Statistical Mechanics (Springer-Verlag, New York, 1995), pp. 64–67: Clausius–Clapeyron equation (eqs 3.13–3.14) and the vapour pressure of a liquid with constant evaporation heat (Exercise 3.2, eq. 3.15). Method reference; no text, tables or worked examples are reproduced.
- NIST Chemistry WebBook, NIST Standard Reference Database 69 (webbook.nist.gov): a source for the property values you enter; no data are reproduced here.
- IAPWS-IF97, Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (International Association for the Properties of Water and Steam): reference saturation data for water.
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
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.
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
Pressure and the boiling point
In Cryogenic Liquids by the Numbers
What it covers: How tank pressure sets the temperature of a stored cryogen, the Clausius–Clapeyron estimate against NIST data, why liquid from a pressurised cylinder flashes, and a regulator set too high.
Useful alongside · KEVOS® original book
Saturation pressure and temperature
In Process Chillers by the Numbers
What it covers: Why boiling point follows pressure, the Clapeyron equation checked against NIST R-134a data, reading gauges, superheat and subcooling, and air in a condenser.
Useful alongside · KEVOS® original book
Reading the steam table
In Process Steam by the Numbers
What it covers: Understand saturated steam through its table: absolute pressure and boiling point, sensible and latent heat, specific volume, why steam is distributed high and used low, and wet steam.
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