## November 20, 2011

### 5.19 Boyle's Law

5.19 use the relationship between the pressure and volume of a fixed mass of gas at constant temperature:
$p_{1}V_{1}=p_{2}V_{2}$

p1 = Pressure at the beginning
V1 = Volume at the beginning
p2 = Pressure at the end
V2 = Volume at the end

NB: Can use any units for V and p as long as they are constant at the beginning and end.

Watch the video below:

We can clearly see that as we reduce the pressure in the vacuum the volume of the gas increases significantly, also note that the Volume is constant and the mass of the gas is constant.

While we’re on the topic of a vacuum, you might like to take a look at the video below “Nothing” by Vsauce a great YouTube channel for quirky science videos:

Conclusion: Pressure is inversely proportional to volume $p\propto \frac{1}{V}$

### 5.18 Gay-lussac's law

5.18 use the relationship between the pressure and Kelvin temperature of a fixed mass of gas at constant volume:
$\frac{p_{1}}{T_{1}} = \frac{p_{2}}{T_{2}}$

p1 = Pressure at the beginning

T1 = Absolute temp at the beginning

p2 = Pressure at the end
T2 = Absolute temp at the end
NB: The units of temperature must be Kelvin, but any unit of pressure can be used
Pressure is directly proportional to absolute temperate (when gas is at a constant volume)
$p\propto T$

### 5.17 Kelvin and Pressure

5.17 describe the qualitative relationship between pressure and Kelvin temperature for a gas in a sealed container.

Increasing the temperature of particles in a sealed container causes them to move with larger amounts of kinetic energy so collide with the walls more often and at higher speeds, this means that when the particles come into contact with the container they apply a larger amount of force onto the area and therefore the pressure increases

Increase in temperature results in an increase in pressure (if volume is constant)
Example: Cloud formation

• Place a little water in the bottom of a 1½ litre plastic bottle
• Squeeze a few times
• Introduce a small amount of smoke
• Squeeze and release several times
• When you squeeze, the cloud disappears; when you release the cloud reforms.
Explanation

• When the pressure increases the temperature increases and vice versa.
• The smoke particles are nucleating sites on which the water can condense
Use the Java app below to test the idea.

 Click to Run

### 5.16 Kelvin and Kinetic energy

5.16 understand that the Kelvin temperature of the gas is proportional to the average kinetic energy of its molecules.

What the graph above shows is that the average speed of the particles squared (v2) is directly proportional to the temperature of the particles in Kelvin. What this means is that as we increase the absolute temperature of the particles we can predict the average speed of the particles.

## November 4, 2011

### 5.15 Temperature and Speed

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

What is Temperature?
Temperature is a measure of the average kinetic energy of the particles in a substance. What this means is that as we increase the temperature of a gas the particles have more kinetic energy and therefore move around at a greater speed and collide with each other more often, it also means that they collide with the walls of the container more often and with a greater force, so looking back at the previous video [see 5.12] an increase in force and a constant surface area results in an increase in pressure \ increase temperature (of a gas) => increased pressure (of the gas).

### 5.14 The Kelvin Scale

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

Describe: The Kelvin scale begins at -273°C and the intervals between Centigrade and Kelvin are equal (i.e. ΔK = Δ°C)

Converting:
To Kelvin: Kelvin = Centigrade + 273

Examples
Convert these temperatures
1. 20°C = 20 + 273 = 293K
2. 150°C = 150 + 273 = 423k
3. 300K = 300 – 273 = 27°C
4. 650K = 650 – 273 = 377°C

### 5.13 Absolute Zero

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

Using particle theory we can explain why the gas in the balloon contracts. Obviously the temperature inside the balloon decreases; meaning that the average kinetic energy of the particles also decreases. If the particles have less KE they will collide with the walls of the balloon with less force (and less collisions per second). Because the walls of the container are flexible, the volume decreases because the particles aren’t applying enough force on the balloon to keep it inflated.

This is known as Charles’ law. A law stating that the volume of an ideal gas at constant pressure is directly proportional to the absolute temperature. $V\propto T$

### 5.12 Gas Molecules

5.12 Recall that molecules in a gas have a random motion and they exert a force hence a pressure on the walls of the container

Watch the video below:

When a gas is introduced to the container the gas particles colldie with all the walls of the container; when particles collide with the wall attached to the needle they have enough force to push the wall and in turn move the needle. The needle on the meter is measuring pressure; as the gas particles collide with the walls they apply a force on the walls, These walls have a surface are, so we can measure the pressure because p=F/A

### 5.11 Brownian motion

5.11 understand the significance of Brownian motion.

What is Brownian motion?
The English Botanist Robert Brown presented the first evidence that matter consists of tiny particles in motion. Brown was studying pollen grains suspended in a liquid with a microscope and noticed the haphazard movement of the grains, this similar motion can also be seen when smoke particles in air are observed under a powerful microscope. The zigzag motion is due to unequal bombardment between the suspended particles and the molecules of the surrounding medium. This irregular motion of suspended particles is known as Brownian motion.

Why is it significant?
Brownian motion was the first step into proving atomic theory, and although it was Einstein that finally described the physics behind the phenomenon, the motion was named after Brown because he was the first to test this theory. So without Robert Brown, we may perhaps have not had such a conclusive theory until a much later date, or we may have had a different theory all together.

The video below visually explains the motion: the Red disc represents large smoke molecules and the small ball bearings represent the small particles that are usually to small to see.