# What would happen if I put a wet/dry bulb hygrometer in supersaturated air (RH > 100%)? Would the wet bulb read hotter than the dry?

Answers to Why is there a maximum humidity? address the thermodynamics of water vapor in air, and the Earth Science SE question How is relative humidity determined from a wet and dry bulb readings? and its answers address how a wet/dry bulb hygrometer works and how to convert the readings to a relative humidity (RH).

Usually the wet bulb is a few degrees C cooler than the dry bulb, and when they read nearly the same temperature (which happens more frequently than I'd like where I live) you know the RH is approaching 100%.

What would happen if I put a wet/dry bulb hygrometer in supersaturated air (RH > 100%)? Would the wet bulb's temperature pass through the dry bulb's and end up reading hotter than the dry bulb's temperature?

my photo; click for full size

From the Earth Science SE question How is relative humidity determined from a wet and dry bulb readings? To get a numerical value for humidity with this set up you use the coarse table on the front (there's a finer table on the back of the box) and look up the dry bulb temperature and the dry minus wet difference to find an approximate humidity. For example If I look up 19 and 2 °C for those respectively (roughly what's shown in the image) I get about 81% relative humidity.

In normal (unsaturated) air, the bulbs are asymmetric due to the water around the wet bulb. Only the wet bulb can evaporate and cool.

In supersaturated air, there is less asymmetry. Water could condense on both bulbs, warming them. The existing water around the wet bulb doesn't help.

It's possible that the cloth itself could act as a superior condensation site than a bare bulb, but I suspect this will be minimal until the supersaturation is quite high.

• I think it's more in the spirit of the question to imagine a wet/dry bulb thermometer that could overcome the engineering challenge of condensation on the dry bulb. Maybe the apparatus vibrates, or there's a strong fan, so that the dry bulb's droplets fall off; or maybe the dry bulb has some hydrophobic coating, which makes condensation on that surface less likely.
– rob
Commented Jan 14, 2023 at 23:06
• @rob you are right, but I didn't really appreciate the issue until you spelled it out so clearly; in a supersaturated (i.e. condensing) environment, they'd both be wet bulbs so the temperature difference would tend towards zero. A mechanism to continuously remove condensation from the "dry" bulb in order to keep it dry might complicate the situation to the point that it doesn't have a simple answer.
– uhoh
Commented Jan 14, 2023 at 23:13
• @uhoh I have a vague recollection that the heat released by condensing droplets helps to drive updrafts in cloud formation. However, I can’t quite come up with a good explanation; I suspect that there may be different types of cloud where the convective heat transport is different, and I’m not ready to invent a theory of weather just to answer this question.
– rob
Commented Jan 15, 2023 at 2:27
• @rob That is accounted for by the definition of entropic temperatures or approximate (ice-)liquid potential temperatures that become the conservative variables instead of the potential temperature (which is the measure of entropy for dry air) and by the the process of computing the virtual potential temperature from the conservative temperature variable and the specific humidities of individual phases of water. E.g. in journals.ametsoc.org/view/journals/atsc/50/23/… or in more modern and more involved schemes. Commented Jan 16, 2023 at 15:21
• Specifically, with the linearized Betts liquid temperature one gets $\theta = \theta_l + \frac{L_v}{c_p} (p_\mathrm{ref}/p)^{R_d/c_p} q_l$ so the second term on the r.h.s. is how warmer the air with liquid water is compared to the air where the water is only in the vapour. Then one computes the effect on the density through the virtual pot. temperature because water vapour is lighter than the air. Commented Jan 16, 2023 at 15:28