Boiling point of water under vacuum: calculator and vapour pressure table

Water boils when its vapour pressure equals the pressure above it. Lower the pressure and water boils at a lower temperature: at 1013.25 mbar (standard atmospheric pressure) it boils at 99.97 °C, at 200 mbar at 60.1 °C, at 100 mbar at 45.8 °C, at 50 mbar at 32.9 °C and at 10 mbar at 7.0 °C.

The same curve can be read the other way round: the vapour pressure at a given temperature is the pressure at which water of that temperature boils. Water at 20 °C has a vapour pressure of 23.4 mbar. Once the pressure in a vessel falls below that value, water at room temperature starts to boil.

All pressures here are absolute pressures. If a gauge shows pressure relative to the surroundings, convert it to absolute pressure first. The unit converter changes pressure units, and the calculator overview lists further tools.

Boiling point of pure water at common absolute pressures. Below the triple-point pressure of 6.11657 mbar there is no stable liquid water, so the last rows give the temperature at which ice sublimes at that pressure.

Calculated with the IAPWS equations (see sources) and rounded. 1 Torr = 1/760 of a standard atmosphere = 1.33322 mbar.

Vapour pressure from −40 °C to 200 °C. Below 0.01 °C the table gives the sublimation pressure of ice, above it the vapour pressure of liquid water.

At 0 °C, supercooled water that is still liquid has a slightly higher vapour pressure than ice: 6.1121 mbar instead of 6.1115 mbar. Above 99.97 °C the vapour pressure exceeds standard atmospheric pressure, so water only stays liquid under overpressure, as in a boiler.

The chart plots pressure on a logarithmic scale against temperature. Left of the triple point lies the sublimation curve of ice, right of it the boiling curve of water. Above the curves water is solid or liquid, below them it is a gas.

At the triple point, 0.01 °C and 6.11657 mbar, ice, liquid water and water vapour are in equilibrium. At lower pressures there is no stable liquid water: ice turns directly into vapour. This is called sublimation.

Freeze drying is based on this. The frozen product is kept at a pressure below the sublimation pressure of its ice, for example below 1.03 mbar at −20 °C or below 0.13 mbar at −40 °C. The vapour flows to an even colder surface, the condenser, where it freezes out again. The heat of sublimation has to be supplied from outside; otherwise the product keeps cooling and drying slows down.

For this range the calculator uses the IAPWS equation for the sublimation pressure of ice (valid from 50 K, i.e. −223.15 °C).

At standard atmospheric pressure (1013.25 mbar = 760 Torr) pure water boils at 99.974 °C, i.e. 373.124 K. This value applies on the International Temperature Scale of 1990 (ITS-90), which is in use today, and is given in the IAPWS tables. 100 °C is a rounded figure.

Conversely, at exactly 100 °C the vapour pressure of water is 1014.18 mbar. The difference of 0.026 K does not matter in the kitchen, but it does for precise measurements. Air pressure matters far more: where it is low, in the mountains for example, water boils well below 100 °C. The calculator above gives the value for your pressure.

Vacuum drying

Under vacuum, water evaporates at a low temperature: at 50 mbar it boils at just 32.9 °C. This allows heat-sensitive products to be dried gently. The heat of evaporation still has to be supplied: without heating, the material cools down until its vapour pressure equals the pressure in the chamber.

Degassing liquids

Degassing is meant to remove dissolved gases, not to evaporate the water itself. Once the pressure reaches the vapour pressure of the liquid, about 23.4 mbar for water at 20 °C, the water starts to boil and produces a lot of vapour, which the vacuum pump then has to handle.

Distillation and evaporation

Under vacuum the boiling point drops: at 100 mbar water boils at 45.8 °C, at 200 mbar at 60.1 °C. This protects products that do not tolerate high temperatures.

Water vapour in the vacuum pump

A vacuum pump that discharges to atmosphere compresses the gas it draws in to above atmospheric pressure. During compression, water vapour condenses as soon as its partial pressure reaches the vapour pressure at the temperature inside the pump. In oil-lubricated rotary vane pumps the condensate mixes with the oil. With gas ballast, air is admitted during compression: the gas mixture reaches discharge pressure before the water vapour reaches its saturation pressure, and the vapour is expelled instead of condensing. Manufacturers state how much vapour a pump can handle this way as its water vapour tolerance in mbar.

Liquid ring pumps work with an operating liquid, usually water. The attainable inlet pressure lies between atmospheric pressure and the vapour pressure of that liquid. Water at 15 °C has a vapour pressure of 17.1 mbar; the pressure reached in practice is higher. A condenser upstream of the pump can remove the vapour before it reaches the pump.

More on this: oil-lubricated rotary vane vacuum pumps, liquid ring vacuum pumps, screw vacuum pumps and the overview of all vacuum pumps. For an application with a lot of water vapour, contact us.

For liquid water between 0.01 °C and 373.946 °C the calculator uses the saturation equations of the industrial formulation IAPWS-IF97 (equations 30 and 31). Both directions come from the same equation and are fully consistent with each other. They reproduce the triple point (273.16 K; 611.657 Pa), the normal boiling point and the critical point (647.096 K; 22.064 MPa).

p_s = 1 MPa · (2C / (−B + √(B² − 4AC)))⁴ with A = ϑ² + n₁ϑ + n₂, B = n₃ϑ² + n₄ϑ + n₅, C = n₆ϑ² + n₇ϑ + n₈ and ϑ = T/K + n₉ / (T/K − n₁₀)

Below the triple point it uses the IAPWS equation for the sublimation pressure of ice Ih (release R14-08, valid from 50 K to 273.16 K). For the reverse direction, from pressure to temperature, this equation is solved numerically.

ln(p_subl / 611.657 Pa) = θ⁻¹ · (a₁θ^b1 + a₂θ^b2 + a₃θ^b3) with θ = T / 273.16 K

Accuracy: IAPWS estimates the uncertainty of the saturation-pressure equation at no more than about ±0.05% (IAPWS-IF97, Fig. 6). For the sublimation pressure the expanded uncertainty is 0.0011% at the triple point, about 0.08% at −20 °C and about 0.17% at −40 °C. The calculator shows six significant digits; the last of them go beyond the accuracy of the equations.

Cross-check: the vapour-pressure equation of Wagner and Pruß (IAPWS SR1-86) differs from IF97 by at most 0.010% between 0.01 °C and 100 °C, and by at most 0.018% up to the critical point (at 187 °C). That corresponds to at most 0.008 K in boiling temperature.

Check values: before rounding to six digits, the calculation matches the IAPWS check values to every published digit, for example 3.53658941 kPa at 300 K (shown as 3.53659 kPa), 372.755919 K at 0.1 MPa = 1 bar (shown as 372.756 K) and 8.94735 Pa over ice at 230 K.

1. IAPWS R7-97(2012): Revised Release on the IAPWS Industrial Formulation 1997 for the Thermodynamic Properties of Water and Steam (IAPWS-IF97). Section 8, Equations (29) to (31), Tables 34 to 36, Fig. 6; triple point Equation (9), critical point Equations (2) and (3). iapws.org
2. IAPWS R14-08(2011): Revised Release on the Pressure along the Melting and Sublimation Curves of Ordinary Water Substance. Equations (1) and (6), Table 3, Fig. 2 and Equation (7a). iapws.org
3. IAPWS SR1-86(1992): Revised Supplementary Release on Saturation Properties of Ordinary Water Substance (Wagner and Pruß). Equation (1) and Table 1, normal boiling point 373.1243 K at 0.101325 MPa. iapws.org
4. NIST Special Publication 811 (2008 edition), Appendix B.8: bar, mbar and standard atmosphere (exact factors); Table 11: 1 Torr = (101 325/760) Pa; Section 4.2.1.1: Celsius temperature t = T − 273.15 K. nist.gov
5. Leybold, Fundamentals of Vacuum Technology: What is a gas ballast and how does it work? Gas ballast, condensation of water vapour in oil-lubricated pumps, water vapour tolerance in mbar. leybold.com
6. Atlas Copco: Liquid ring vacuum pump working principle. Attainable inlet pressure between atmospheric pressure and the vapour pressure of the operating liquid. atlascopco.com