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Gas Laws

The Kinetic Molecular Theory
of Ideal Gases

These statements are made only for what is called an ideal gas. They cannot all be rigorously applied (i.e. mathematically) to real gases, but can be used to explain their observed behavior qualitatively.

1. All matter is composed of tiny, discrete particles (molecules or atoms).

2. Ideal gases consist of small particles (molecules or atoms) that are far apart in comparison to their own size. The molecules of a gas are very small compared to the distances between them.

3. These particles are considered to be dimensionless points which occupy zero volume. The volume of real gas molecules is assumed to be negligible for most purposes.

This above statement is NOT TRUE. Real gas molecules do occupy volume and it does have an impact on the behavior of the gas. This impact WILL BE IGNORED when discussing ideal gases.

4. These particles are in rapid, random, constant straight line motion. This motion can be described by well-defined and established laws of motion.

5. There are no attractive forces between gas molecules or between molecules and the sides of the container with which they collide.

In a real gas, there actually is attraction between the molecules of a gas. Once again, this attraction WILL BE IGNORED when discussing ideal gases.

6. Molecules collide with one another and the sides of the container.

7. Energy can be transferred in collisions among molecules.

8. Energy is conserved in these collisions, although one molecule may gain energy at the expense of the other.

9. Energy is distributed among the molecules in a particular fashion known as the Maxwell-Boltzmann Distribution.

10. At any paticular instant, the molecules in a given sample of gas do not all possess the same amount of energy. The average kinetic energy of all the molecules is proportional to the absolute temperature.

 
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CHARLES'S LAW

 

Again we start with the Combined Law to get Charles's Law, but now there is no change in the pressure volume, so P1 = P2.

 

P1 V1 = T1
P2 V2   T2

 

If you cancel out the two pressures, you get a form of Charles's Law that I consider easiest to remember. You can still see the P V = n R T in it if you look hard enough.

 

V1 = T1
V2   T2

KNOW THIS

 

You may have seen this written differently, as in the following form:

V1 = V2
T1   T2

 

These two expressions are mathematically exactly the same, but the first one shows its origin in the Combined Law. Remember it by, "Charles is under constant pressure."

To get a better feeling for Charles's Law, consider a child's toy balloon. At points between the beginning of filling of a balloon and the maximum stretching of a balloon, the change in internal pressure of a balloon is negligible as the balloon increases in size. A balloon is partially filled at room temperature and placed in the sun inside a car on a hot day in summer. The balloon expands in proportion to the Kelvin temperature. When the same balloon is take out of the car and put into a home freezer, the volume of the balloon decreases.

 

 

Back to the top of Gases.

 

Boyle's Law is useful when we compare two conditions of the same gas with no change in temperature. (Remember, "Always Boyle's at the same temperature!") No change in temperature means T1 = T2, so we can cancel the two temperatures in the Complete Gas Law Formula and get:

 

P1 V1  = 1       or                  P1 V1 = P2 V2
P2 V2                     the usual Boyle's Law

 

P1 V1 = P2V2

KNOW THIS

 

The usual expression of Boyle's Law was lurking right there in the Combined Gas Law Formula. As you can see, Boyle's Law is in the classic form of, "P is inversely proportional to V." We could predict that from the P and V being together in the numerator of the same side of the equation.

To get a feel for Boyle's Law, visualize a small balloon between your hands. The balloon is so small that you can push all sides of it together between your hands without any of the balloon pouching out at any point. When you push your hands together the volume of the gas in the balloon decreases as the pressure increases. When you let up on the pressure, the volume increases as the pressure decreases.

 

THE THIRD LAW

 

The third gas law from the Combined Gas Law has been named for Gay-Lussac in some books, Amonton in others, and not named in a large number of books. It is sometimes amusing to read a book that does not name the third law and needs to refer to it. The third law is the relationship of pressure and temperature with constant volume (V1 = V2.) the pressure and absolute temperature of a gas are directly proportional.

 

P1 V1 = T1
P2 V2   T2

 

And so we get the third law, the relationship between the pressure and temperature of a gas.

 

P1 = T1
P2   T2

KNOW THIS

 

Similarly to Charles's Law, it can be arranged so that it appears in the same form you see in most books.

P1 = P2
T1   T2

 

To get a feel for the third Law, consider an automobile tire. With a tire gauge measure the pressure of the tire before and immediately after a long trip. When cool, the tire has a lower pressure. As the tire turns on the pavement, it alters its shape and becomes hot. There is some expansion of the air in the tire, as seen by the tire riding slightly higher, but we can ignore that small effect. If you were to plot the temperature versus pressure of a car tire, would zero pressure extrapolate out to absolute zero? Remember what you are measuring. The pressure of a car tire is actually the air pressure above atmospheric pressure. If you add atmospheric pressure to your tire gauge, you would certainly come closer to extrapolating to absolute zero

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