Ideal gas molecules

Section 5: d) Ideal gas molecules

5.11 understand the significance of Brownian motion

Go to this applet: http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html

So you see the random or irregular motion of the smoke/dust particle (blue)? The small air particles (red) are constantly bombarding it, making it move. That is called Brownian motion. Note that it only happens in fluids, a fluid is any substance that has the ability to flow or move freely (e.g. gas/liquid). 

When the scientists look under the microscope, they observed the smoke particle to be moving irregularly and deduced that there were air molecules that were too small to be seen that were colliding with it. The smoke particles, being much larger than the air molecules, are continually bombarded unevenly on different sides by the air molecules and this bombardment is what results in the irregular movement of the smoke particles. 

Brownian motion: The random movement of microscopic particles in a fluid, as a result of continuous bombardment from molecules of the surrounding medium. 

5.12 recall that molecules in a gas have a random motion and that they exert a force and

hence a pressure on the walls of the container

Gas molecules move randomly but in straight lines, and when they collide with the inner walls of the container they are held in, they exert a force. And there are a large number of gas molecules, thus at any one time there are numerous such collisions taking place between the air molecules and the wall. 

If we add up and find the average of all the forces from such collisions, we can find the average force that is acting on the wall. Since pressure is force per unit area (pressure=force/area), the gas is exerting a pressure on the container's wall!

So basically, you can conclude that the pressure of a gas is due to collisions of gas molecules with the walls of the container. 

5.13 understand that there is an absolute zero of temperature which is –– 273°C

Just remember this value as the absolute zero. It is the lowest temperature on Earth.

5.14 describe the Kelvin scale of temperature and be able to convert between the Kelvin

and Celsius scales

Please ignore the Fahrenheit and Rankine bit.

To convert from Kelvin to Celsius and back, just use:

K = °C + 273.15

°C = K - 273.15

5.15 understand that an increase in temperature results in an increase in the speed of gas

molecules

So just understand that increasing temperature means that the gas molecules move faster. This is because a larger amount of thermal energy is converted to kinetic energy of the air molecules. (i.e. the gas molecules have more kinetic energy). This will cause the molecules to move faster.

5.16 understand that the Kelvin temperature of the gas is proportional to the average

kinetic energy of its molecules (Single science)

5.17 describe the qualitative relationship between pressure and Kelvin temperature for a

gas in a sealed container

So you know that a rise in temperature of air causes an increase in the speed of the air molecules. The air molecules will then bombard the walls of the container more vigorously and more frequently. This means that the average force acting on the inside wall of the container due to the air molecules increases. As the volume of the container is fixed, this will result in an increase in pressure inside the container.

5.18 use the relationship between the pressure and Kelvin temperature of a fixed

mass of gas at constant volume: (single science)

p₁/T₁ = p₂/T₂

5.19 use the relationship between the pressure and volume of a fixed mass of gas at

constant temperature:

p1V1 = p2V2

Boyle's Law: pV=k (k is a constant)

This is when the temperature is kept constant.

This means that pressure is indirectly proportional to volume. i.e. p ∝ 1/V

So when a graph of p against V is plotted, you get a smooth curve. But if you plot p against 1/V, a straight line is obtained. 

I'll explain this relationship to help you understand:

If you halve the volume of a container, you're doubling the number of molecules per unit volume. --> The same number of molecules have to occupy a space half the original size. 

This would mean that the frequency of collisions of the molecules with the walls of the container will also be doubled. Hence the pressure will double. 

If the whole inverse thing confuses you, just remember the original equation pV=k. I'll admit the inverse stuff sometimes confuses me too. :/

pV=k, so to maintain a constant, if you increase volume, pressure decreases. And if you decrease volume, pressure increases. I find this easier to understand. :D