This is the second of a series of articles in our Vacuum Heat-Treatment Series. This part is intended to teach us all about how gases behave in a vacuum environment, look at the equations needed to explain their behavior and explore what happens when we pump down a vacuum vessel. It is important to understand something about the Theory of Gases since a vacuum environment is hardly a space containing” nothing at all.” What remains inside the vacuum vessel will definitely affect the component parts we process.
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| Fig. 1. Molecules on the move[1]
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In vacuum heat, we are always dealing with the movement of gases. So, everyone needs to understand something about the nature (theory) of gases and how they behave, especially in vacuum. The main difficulty, however, is that too much theory tends to become a distraction. Our mission is to learn how these equations help us understand what goes on inside a vacuum vessel.
We begin with the realization that any gas can be completely described in terms of the following quantities:
- Pressure (P)
- Volume (V)
- Temperature (T)
- Number of molecules (n)
The Gas Laws, therefore, are formulas that simply allow one to find the value of one of these quantities if you know the others. Let’s review them.
1. Boyle’s Law: P
1V
1 = P
2V
2 This formula tells us that if the temperature is held constant, the increase in pressure is exactly proportional to the decrease in volume.
2. Charles’ Law: P
1/T
1 = P
2/T
2 This formula tells us that an increase in pressure is directly proportional to the increase in the absolute temperature if the volume is held constant.
3. Avogadro’s Law: P
1/n
1 = P
2/n
2 This formula tells us that equal volumes of any gas at the same temperature and pressure contain the same number of molecules.
4. Ideal Gas Law: PV = nRT
This formula relates all four of the quantities needed to completely describe the state of a gas. Here R is a constant known as the universal gas constant and has a value of 62.4 torr-liter/mole-°K.
Another useful gas law is the law of partial pressure.
5. Dalton’s Law: P
TOTAL = P
1 + P
2 + … + P
nThis formula tells us that in a mixture of gases where the gases do not react chemically, each gas exerts its own pressure independently as if no other gases were present.
Other characteristics that help describe the behavior of gases in a vacuum environment include:
- The kinetic theory of gases
- Mean free path of molecules
- Phase change
- Evaporation
- Condensation
- (Dynamic) equilibrium
- Vapor (partial) pressure
- Gas flow
- Resistance to gas flow
- Gas conductance
Let’s briefly consider several of these characteristics.
The Kinetic Theory of Gases This theory is used to explain the behavior of gases in terms of the behavior of the individual gas molecules. Gases are in constant motion. Hence, it makes sense to discuss their kinetic nature. Remember also that gases are free to wander throughout the space available to them. So, the temperature of a gas is simply a measure of this kinetic nature of the particles (their kinetic energy). The higher the temperature, the faster and faster the molecules move and the greater their kinetic energy.
By comparison, pressure is related to the number of collisions of molecules against the walls of their container. An increase in temperature causes molecules to hit harder and more often, creating even higher pressure (in accordance with Charles’ Law). Similarly, a decrease in temperature causes molecules to hit less hard and less often, resulting in lower pressure.
If you were to remove some of the gas from the vacuum vessel, fewer molecules are left to make contact with the walls and the pressure is lower (in accordance with Avogadro’s Law and the Ideal Gas Law). Decreasing the volume of gas (at constant temperature) results in a reduced area where the original number of molecules strike and causes the pressure to increase (in accordance with Boyle’s Law).
Mean Free Path
The mean free path, or distance between molecules, can be calculated from the kinetic theory as follows:
6.
l = 1/√2πD2nwhere
l is the mean free path in centimeters, D is the diameter of the gas molecule in centimeters and n is the number of gas molecules per cubic centimeter.
What is important is that this formula tells us that pressure, which is proportional to the number of molecules per unit volume (in accordance with the Ideal Gas Law), is inversely proportional to the mean free path. As the pressure decreases, the mean free path between molecules increases.
Phase ChangeIf we change the state of matter by changing the temperature or pressure (or both), we change the phase in which it exists. In vacuum, as we pump down, we reduce the pressure and temperature and convert the moisture in the air to solid ice.
Dynamic Equilibrium and Vapor Pressure
When the number of molecules leaving a part surface is equal to the number of molecules returning to it (when the rate of evaporation equals the rate of condensation), the system is said to be in dynamic equilibrium. The partial pressure of the vapor at which it occurs is the vapor pressure of the material.
Gas Flow The rate at which gas flows through the vacuum vessel into the pump is important in vacuum systems. This determines the time required to reach operating pressure and may ultimately determine the system’s tolerance to leaks and outgassing.
