Unit 5: Solids, Liquids and Gases: Chapter 19: Solids, Liquids and Gases

Random Motion and Pressure: Molecules in a gas have random motion and exert a force, hence pressure, on the walls of a container.
Absolute Zero:
- There's an absolute zero of temperature: $-273$ °C.
Kelvin Scale:
- Describes the Kelvin scale of temperature.
- Able to convert between Kelvin and Celsius scales.
Temperature and Speed: An increase in temperature results in an increase in the average speed of gas molecules.
Kelvin Temperature and Kinetic Energy: The Kelvin temperature of a gas is proportional to the average kinetic energy of its molecules.
Qualitative Relationships (Fixed Gas Amount):
- Pressure and volume at constant temperature.
- Pressure and Kelvin temperature at constant volume.
Pressure and Kelvin Temperature Relationship (Fixed Mass, Constant Volume):
- $\frac{P1}{T1} = \frac{P2}{T2}$
Pressure and Volume Relationship (Fixed Mass, Constant Temperature):
- $P1V1 = P2V2$

Matter in Motion: All matter is made of continuously moving particles; arrangement and movement determine material properties.
Gas Laws: Laws describe the relationship between pressure, temperature, and volume.
Brownian Motion: Observation made by botanist Robert Brown, leading to the kinetic theory of matter.

Particle Movement: Gases consist of molecules moving in a random, haphazard way.
Pressure Exertion: Molecules hitting container walls exert a force; combined collisions result in pressure.

Robert Boyle's Discovery: Air is "squashy," and springs back when compressed; demonstrated using a bicycle pump or syringe.
Experiment: Boyle studied how gas volume depends on exerted pressure, keeping temperature constant.
Pressure Measurement: Pressure is force per unit area, measured in N/m² or pascals (Pa).
Gas Compression: Gases can be compressed because molecules are spread out; squeezing into a smaller container increases pressure.
Particle Theory Explanation: At constant temperature, average particle speed is the same; squeezing into smaller volume causes more frequent collisions, increasing average force and pressure.
Observation: Doubling the pressure halves the volume.
Boyle's Law Equation: $P1V1 = P2V2$
- For a fixed gas mass, changing pressure or volume results in the same product of $p \times V$ if temperature remains constant.
Example Calculation:
- Atmospheric pressure is $100$ kPa. Air in a sealed container has a volume of $2 m^3$ at atmospheric pressure. Reducing the volume to $0.2 m^3$ would result in a pressure of $1000$ kPa.

Temperature Impact: Temperature affects gas pressure. Experiment involves measuring pressure of a fixed gas volume at varying temperatures.
Pressure-Temperature Relationship: Gas pressure increases with temperature and decreases with cooling.
Absolute Zero Concept: Cooling gas leads to decreased pressure; a temperature exists below which cooling is impossible: absolute zero.
Absolute Zero Value: Approximately $-273$ °C.

Starting Point: Starts from absolute zero.
Proportionality: Kelvin temperature is proportional to the average kinetic energy of molecules.
Conversion Formulas:
- Temperature in K = Temperature in °C + 273
- Temperature in °C = Temperature in K - 273
Example Conversions:
- Water freezes at $0$ °C = $273$ K.
- Room temperature (20°C) = 293 K.
- $400$ K = $127$ °C.
Pressure vs. Kelvin Temperature Graph: Straight line through the origin, indicating proportionality.
Temperature Doubling: Heating gas from $200$ K (-73°C) to $400$ K (127°C) doubles its pressure.
Example Calculation
- An empty tin is heated using a Bunsen burner until the temperature of the air inside is $50$ °C. Find the pressure of the air inside the tin. The temperature of the room is $20$ °C.
- p2 = $100 kPa \times \frac{323 K}{293 K} = 110 kPa$
Explanation for relationship:
- Heating a gas increases particle speed, resulting in harder and more frequent collisions with container walls, increasing average pressure.
Cooling Effect:
- Cooling decreases kinetic energy; at absolute zero, particles have no thermal/movement energy, so they cannot exert pressure.
Temperature Symbol:
- $T$ for Kelvin, remember to convert Celsius to Kelvin when using gas law equations involving temperature changes.
Fixed Mass, Constant Volume Relationship:
- $\frac{P1}{T1} = \frac{P2}{T2}$

NB T must be measured in Kelvin.

The formulas included in the note are: