Reviewing the laws of physics that govern water vapor in a moist gas can help you better understand the properties of what you’re measuring. Understanding these properties will help you make a more accurate measurement and do your job more effectively, whether it’s protecting a product from corrosion or maintaining a precise environment for storage or manufacturing.
Humidity and Laws of Physics
From pressure to temperature, the following ideal gas laws help us understand how humidity levels shift depending on the environment.
Definition:
Standard Temperature and Pressure (STP) is set at a temperature of 0 °C, 32 °F and a pressure of 101.3 kPa at one atmosphere.
| Name | Definition | Law | Notes |
|---|---|---|---|
| Boyle’s Law | At constant temperature, the product of the volume and pressure of a given amount of gas is a constant. | P x V = constant | The value of the constant depends on how much gas is in the volume. |
| Charles’s Law | At constant pressure, the volume of a given quantity of gas is proportional to absolute temperature (K). Or at constant volume, the pressure of a given quantity of gas is proportional to absolute temperature. | V= q x T Or P= j x T | q is a proportionality constant that depends on the quantity of gas. j is a proportionality constant that depends on the particular sample of gas and its volume. To convert temperature in °C into absolute temperature in K, add the constant 273.15. |
| Dalton’s Law of Partial Pressures | The total pressure of a mixture of gases is equal to the sum of the pressures that each gas would exert if it were present alone. | Pt = P1+ P2+ P3+... | P1, P2, etc., are the partial pressures of gases 1, 2, etc. |
| Avogadro’s Hypothesis | Equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. | Example: one liter of any ideal gas at a temp. of 0 °C and a pressure of 101.3 kPa, contains 2.688 x 1022 molecules. | The temperature of 0 °C and pressure of 101.3 kPa is the standard temperature and pressure condition or STP. |
Definition:
It has been experimentally determined that the number of atoms in 12 grams of 12C is 6.022 x 1023.This number is called Avogadro’s number.
Mole Fractions and Partial Pressure
Mole Fractions and Partial Pressure The composition of one mole of a gas mixture can be expressed in terms of the mole fractions of its components. The mole fraction of a particular component is defined as the total number of moles of the component divided by the total number of moles of all the components. From this definition, it follows that the sum of all mole fractions is equal to one.
| Name | Definition | Law | Notes |
|---|---|---|---|
| Volume of a Mole of Gas at Standard Temperature and Pressure (STP) | As one liter of gas at STP contains 2.688 x 1022 molecules (or atoms in the case of a mono atomic gas), it follows that a mole of gas (6.022 x 1023 molecules) occupies a volume of 22.4 l at STP. | See definitions of mole and Avogadro’s number below. | |
| Ideal Gas Law constant. | The product of volume and pressure of a given amount of gas is proportional to absolute temperature. | P x V = n x R x T | n is the number of moles of gas and R the molar gas constant. The constant R is equal to: 0.08206 atm x liter/K x mole 8.30928 Pa x m3/K x mole |
Definition:
A mole of any element is defined as the amount of that element that contains the same number of molecules (or atoms in the case of a mono atomic element) as exactly 12g of 12C (Carbon 12).
Example: Dry air near sea level
- Nitrogen: Mole Fraction: 0.78084
- Oxygen: Mole Fraction: 0.20948
- Carbon Dioxide: Mole Fraction: 0.0004
If Pt is the total pressure of a gas mixture and n1, n2, etc. the mole fractions of its components, it follows that:
Pt= Pt x (n1+ n2 + ...) and
Pt= Pt x n1+ Pt x n2 + ...
where Pt x n1, Pt x n2, etc. are the partial pressures of components 1, 2, etc.
The equation above is another form of Dalton’s law.
Learn more about humidity in the following video: “Relative Humidity Measurement Explained”
See related blog posts:
Theory 1 – What is Humidity?
Theory 2 – Relative Humidity, Pressure and Temperature
Theory 3 – Humidity and Vapor Pressure
Theory 4 – Definitions of Humidity: Vapor Concentration
Theory 5 – Effect of Temperature and Pressure on % rh
Theory 6 – Humidity Academy Theory 6 – The Capacitive Sensor
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