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### Water Vapor Saturation Pressure Formulae and Calculator

Water Vapor Saturation Pressure

Increasing temperature of liquid (or any substance) enhances its evaporation that results in the increase of vapor pressure over the liquid. By lowering temperature of the vapor we can make it condense back to the liquid. These two phase transitions, evaporation and condensation, are accompanied by consuming/evolving enthalpy of transition and by a change in entropy of the material.

The water vapor saturation pressure is required to determine a number of moist air properties, principally the saturation humidity ratio. Saturated water vapor pressure is a function of temperature only and independent on the presence of other gases. The temperature dependence is exponential. For water vapor the semi empirical dependence reads as :

Equation 1
pw, s = eA + B/T + C lnT +Dt

Where:

pw, s = water vapor saturation pressure (Pa)
T = Temperature in Kelvin, K = °F + 255.927778
A = 77.34,
B = -7235,
C = - 8.2,
D = 0.005711,
e = 2.718281828,
t = saturation temperature

Reference:
Lecture Notes
Sampo Smolander
University of Helsinki

Alternative (recommended) formula given by IPAWS R7-97(2012) and R14-08 (2011). The saturation pressure over liquid water for the temperature range of 32 to 392°F is given by:

Equation 2
ln pw, s = C8/T + C9 + C10T + C11T2 + C12T3 + C13 ln T

Where:

pw, s = saturation pressure, psia
T = absolute temperature, °R = °F + 459.67
C8 = –1.0440397 E+04
C9= –1.1294650 E+01
C10 = –2.7022355 E–02
C11 = 1.2890360 E–05
C12 = –2.478068 1 E–09
C13 = 6.5459673 E+00

The coefficients of Equations (2) were derived from the Hyland-Wexler equations, which are given in SI units.

Above the surface of liquid water there always exists some amount of gaseous water and consequently there exists a vapor pressure. When a container containing water is open then the number of the escaping molecules is larger than the number of molecules coming back from the gaseous phase (Fig. 1). In this case vapor pressure is small and far from saturation. When the container is closed then the water vapor pressure above the surface increases (concentration of molecules increases) and therefore the number of molecules coming back increases too (Fig. 2). After some time, the number of molecules escaping the liquid and that coming back becomes equal. Such situation is called by dynamic equilibrium between the escaping and returning molecules (Fig. 3). In this case, it is said that the water vapor pressure over the liquid water is saturated.

Figues 1, 2 and 3

Table 1 - Derived from Equation 2

 Temperature Saturation Pressure ˚ F ˚ R psia Pa 32 491.7 0.0886 611.21 44 503.7 0.1420 979.27 56 515.7 0.2220 1530.79 68 527.7 0.3392 2338.80 80 539.7 0.5074 3498.08 92 551.7 0.7439 5129.31 104 563.7 1.0709 7383.46 116 575.7 1.5151 10446.37 128 587.7 2.1093 14543.35 140 599.7 2.8926 19943.75 152 611.7 3.9110 26965.43 164 623.7 5.2183 35978.96 176 635.7 6.8765 47411.59 188 647.7 8.9562 61750.80 200 659.7 11.5374 79547.49 212 671.7 14.7095 101418.67 224 683.7 18.5720 128049.71 236 695.7 23.2345 160196.16 248 707.7 28.8168 198685.05 260 719.7 35.4495 244415.77 272 731.7 43.2735 298360.56 284 743.7 52.4405 361564.68 296 755.7 63.1126 435146.16 308 767.7 75.4625 520295.41 320 779.7 89.6731 618274.54 332 791.7 105.9380 730416.57 344 803.7 124.4604 858124.52 356 815.7 145.4541 1002870.48 368 827.7 169.1422 1166194.58 380 839.7 195.7580 1349704.14 392 851.7 225.5442 1555072.74

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