# How does relative humidity affect the rate of water evaporation?

How does the relative humidity of the air affect the speed at which water evaporates? I know there are other parameters that affect it, so I made this assumptions:

We have a plain metal plate of $1m^2$at a constant temperature $T$, with a thin layer of water above it, the temperature of the water is the same as the metal plate. There is no wind ($v_{air}=0m/s$). The relative humidity of the air is a constant $0<h<100$%. The temperature of the air $T_{air}$ is greater than $T$. The amount of water we have is $w$.

In this simplified case, how would the relative humidity of the air affect the speed at which water evaporates?

• At 100% relative humidity in a closed container (environment) there will be no net evaporation of water - the liquid is in thermodynamic equilibrium with the water vapor in the gas phase. – Jon Custer May 3 '17 at 19:23
• If your aim is to calculate the rate of evaporation of water from the information you have given, then you're in for a very tough problem. For one, you can't just assume that the relative humidity of air above the water is at some fixed constant. In actuality, a thin layer of air immediately above the water will become saturated with humidity, and further significant evaporation will be very sensitive to any slight breezes or winds which blow away this saturated air layer. – Samuel Weir May 3 '17 at 19:37
• This will perhaps help: physics.stackexchange.com/questions/259120/… – Deep May 4 '17 at 4:24

## 1 Answer

The evaporation rate can be calculated but with a quite complex diffusion differential equation.

@Samuel is correct that you cannot assume a uniform distribution of humidity. There is water density variation in space. The gradient is the driving force to move water vapor away from the water surface and to maintain the evaporation process.

The water density is higher close to the water surface. On the surface, we may assume it to be at vapor pressure in most case. If it is less than the vapor pressure, the evaporation is aggressive and if it is more than the vapor pressure, we will see condensation.

When it is at water vapor pressure, the water vapor is then driven out into space under diffusion. If the space humidity is high, the driven force is small that the less water vapor moves into space and vice versa.

There is also heat transfer associated to this evaporation process making it more complicated.