airthermodynamicswater
I'm trying to find a formula that will give me as a result, the amount of water in a cubic meter of air.
I have read this question How to calculate the volume of water in a certain amount of air, given the relative humidity?
The chart works great but I need the formula to input many data.
Someone can help me?
You need a psychrometric chart.
On the x-axis, input the value of a common air thermometer (it's the dry bulb temperature). Now follow a vertical line until you reach the red curve that reads 90% relative humidity.
Follow the horizontal line to the y-axis on the right and that humidity ratio will be the ratio of water versus dry air (mass-wise). That is, 0.015 means that 1.015 kg of your current air has 1.000 kg of dry air plus 0.015 kg of water vapor.
To turn that into volume of water per volume of air (air is different from dry air), you'll have to do a little math and unit conversion. You can use 1.2 kg/m³ as the density of dry air (at 20°C) if it helps.
I'll address one of the key questions you are asking and, I believe, you'll be able to figure the answers to other questions yourself:
After the water vapor has evaporated into the air and the mix has reached the thermal equilibrium through adiabatic process and without outside work done to the whole closed system, what is the relative humidity of the water vapor?
The answer to this question is 100%.
The dynamic equilibrium is achieved when the rate of evaporation is equal to the rate of condensation. Condensation happens when the relative humidity is 100%.
In other words, given enough time, the relative humidity in a closed container with water will become 100%.
This Hyperphysics article contains some empiric formulas and graphs that will help you determine the density of the saturated vapor as a function of temperature.
Best Answer
The Antoine equation will allow you to calculate the vapor pressure of water at a given temperature, which will allow you to calculate the partial pressure of water at 100% relative humidity. Multiplying this partial pressure by the relative humidity will provide the actual partial pressure of water vapor at the given relative humidity. Assuming that water follows the ideal gas law, the number of moles per cubic meter can be calculated, as shown below.
Antoine equation
$\log_{10}(P)=A-\frac {B}{T+C}$,
where P is the vapor pressure of water, in bar
A=5.20389
B=1733.926
C=-39.485
T is measured in Kelvins
Multiply the calculated pressure by 100,000 to convert to Pa. Then, use the ideal gas equation to calculate the number of moles per cubic meter.
$PV=nRT$
$\frac {PV}{RT}=n$
where R = 8.314 $m^3$-Pa/K-mol
This value of "n" corresponds to 100% relative humidity, so multiply by actual relative humidity to get the true value of moles per cubic meter. If you need grams per cubic meter, multiply moles by 18.02.