# What law or formula discusses the relationship between pressure and dew point?

A lot of times, dew point is focused primarily upon temperature and relative humidity. However, that same point of saturation is affected by the pressure, but I can't find a formula, or law even, that discusses this.

It's possible that my premise of the relationship between dew point and pressure may be inaccurate, but if so, how can we then explain that a refrigerant may be a vapor at 210°F in a 280psi container, have a dew point of 125°F, but also be a vapor at 75°F in a 70psi container.

Whether the substance is water, freon, or any liquid, there should be relationships between pressure and dew points (saturation points, condensation points, etc - they're all meaning the same thing). We can clearly see with freon there's some relationship between pressure and temperatures where the rate of condensation is greater than that of the evaporation, but I can't seem to find any laws/formulas for this.

• I'm a bit confused, since in the first paragraph you talk about 'relative humidity' which by default I associate with water, while in the second paragraph you talk about a refrigerant. – Jon Custer Nov 27 '17 at 20:55
• You're right - humidity is confined to water only, but there's lots of other substances that condense/vaporize as well. Perhaps you can substitute my use of "humidity" for "the amount of gas in the air relative to its condensation temperature." If there's a term for that, it may be beneficial to know that and I'll edit the question. The bigger question lies in the 2nd paragraph though. – Tony DiNitto Nov 27 '17 at 21:12
• OK, so now we can clarify that second paragraph. Yes, you can have a substance that would be all vapor at 210F and still have vapor pressure at 75F (in equilibrium over liquid). – Jon Custer Nov 27 '17 at 21:21
• Making this a comment, because I'm not certain, but I think you want the Clausius-Clapeyron relation, which allows you to find the dividing line in a phase diagram. – Sean E. Lake Nov 29 '17 at 23:00
• @TonyDiNitto, research the Antoine equation. This equation establishes the relationship between vapor pressure and temperature for pure substances. See en.wikipedia.org/wiki/Antoine_equation – David White Nov 30 '17 at 1:06

## 3 Answers

For single-component liquids, boiling point = condensation point. Both are the same temperature for a given pressure. Let's talk boiling.

Liquids boil when the vapor pressure of the liquid equals the pressure of the surrounding gas (e.g. 1 atm for open containers at sea level). As you raise the temperature of a liquid, the vapor pressure increases until it equals the pressure of the surrounding gas at which point it boils. If you reduce the pressure of the surrounding gas, then you do not need to raise the temperature of the liquid as much anymore. This is why water boils at 82 C instead of 100 C on Everest-- because the atmospheric pressure is lower:

If you have the vapor pressure $P_1$ of a pure substance at one temperature $T_1$ you can calculate the vapor pressure $P_2$ at a second temperature $T_2$ using the Clausius-Clapeyron equation:

$$\ln\frac{P_2}{P_1} = \frac{-\Delta H_{vap}}{R}\left(\frac{1}{T_2} - \frac{1}{T_1}\right)$$

where
$P$ = vapor pressure
$\Delta H_{vap}$ = enthalpy of vaporization in $J/mol$
$R$ = the gas constant = $8.3145\ J/mol \cdot K$
$T$ = temperature in $K$

Even though I am not an expert on this, I found some information that can help. Check out this website

https://www.vaisala.com/sites/default/files/documents/Dew-point-compressed-air-Application-note-B210991EN-B-LOW-v1.pdf

and this website

https://en.wikipedia.org/wiki/File:Dewpoint.jpg

• This site actually says, "changing the pressure of a gas changes the dew point temperature of the gas." Which is what I've known from observation of Freon gasses, but yet I could never find anyone ever talking about this. – Tony DiNitto Dec 1 '17 at 15:28

The common use of the term "dew point" is actually the "Atmospheric Dew Point" which doesn't take account the pressure of a system, as it's presumed to be at 1 atm. Many readily found formulas on dew point are formulas for atmospheric dew point, as they focus solely on temperature and the amount of gas (eg. water vapor) trapped the air.

The other important variable in what affects dew point is the pressure, which is where Pressure Dew Point (PDP) comes into play.

As a rule of thumb (without the use of complex equations), compression increases/raises the dew point temperature and expansion/decompression lowers the dew point.

This makes sense considering if you have a fixed amount of vapor in the air, and expand/decompress that vapor, the overall percentage of moisture in the air will be smaller, meaning the relative humidity percentage will decrease, and therefore lower the dew point.

At this point, the standard atmospheric dew point formulas can then be applied to find dew points at different levels of pressure.

As an actual example, the dew point for a parcel of air at 200 PSIg would have a dew point at -40°F, whereas the same parcel at 5 PSIg, significantly less compressed than the 200 PSIg parcel, would have a dew point of -77°F.

This has important applications in really understanding how things fully work like heat pumps, air dryers, food processing plants, electronics manufacturing, and more.