Thermal Physics
2.1 Kinetic Particle Model of Matter
##### 2.1.1 States of Matter
Core
1. Distinguishing Properties:
* Solid: Fixed shape and volume. Cannot be compressed.
* Liquid: Fixed volume. Takes shape of container. Cannot be compressed.
* Gas: No fixed shape or volume. Fills container. Can be compressed.
2. Changes of State:
* Melting: Solid → Liquid
* Freezing: Liquid → Solid
* Boiling/Evaporation: Liquid → Gas
* Condensation: Gas → Liquid
* Sublimation (not required but good to know): Solid → Gas directly (e.g., dry ice).*
##### 2.1.2 Particle Model
Core
1. Particle Diagrams & Arrangements:
```plaintext
SOLID: LIQUID: GAS:
• • • • • • • • • • •
• • • • • • • •
• • • • • • • • • •
• • • • • • • • •
• • • • • • • • • •
```
* Solids: Particles close, regular arrangement, vibrate about fixed positions.
* Liquids: Particles close, random arrangement, move around each other.
* Gases: Particles far apart, random arrangement, move rapidly in all directions.
2. Temperature & Motion:
* Temperature ↑ → Average kinetic energy of particles ↑ → Particles move/vibrate faster.
* Absolute Zero: -273°C (0 K). Particles have minimum possible kinetic energy (but not zero energy).
3. Gas Pressure:
* Caused by particles colliding with and exerting a force on the walls of their container.
* More frequent/harder collisions → Higher pressure.
4. Brownian Motion:
* Evidence for kinetic model: Random, jerky motion of smoke particles (microscopic) in air, observed under a microscope.
* Explanation: Caused by random, unequal collisions with faster-moving, invisible air molecules.
Supplement
7. Pressure in terms of Force:
Pressure is the *force per unit area** exerted by the colliding particles. \( p = \frac{F}{A} \)
8. Distinction: Brownian motion involves microscopic particles (e.g., smoke) being moved by collisions with atoms or molecules (e.g., air).
##### 2.1.3 Gases & Absolute Temperature
Core
1. Qualitative Effects:
* (a) Constant Volume, Temperature ↑: Particles gain kinetic energy, move faster. Collide with walls more frequently and with greater force. Pressure increases.
* (b) Constant Temperature, Volume ↑: Particles have same speed but are more spread out. Fewer collisions per second with the walls. Pressure decreases.
2. Temperature Conversion:
* \( T \,(\text{in K}) = \theta \,(\text{in °C}) + 273 \)
* Example: 20°C = 20 + 273 = 293 K
Supplement
3. Boyle's Law:
* For a fixed mass of gas at constant temperature: \( pV = \text{constant} \)
* This means: \( p_1V_1 = p_2V_2 \)
* Graphical Representation: A plot of pressure (p) vs. volume (1/V) is a straight line through the origin.
```plaintext
p
| •
| /
| /
|/_
+-----------> 1/V
```
---
#### 2.2 Thermal Properties & Temperature
##### 2.2.1 Thermal Expansion
Core
1. Qualitative Expansion: Most substances expand when heated.
* Solids: Expand least.
* Liquids: Expand more than solids.
* Gases: Expand most.
2. Applications & Consequences:
* Applications: Bimetallic strip in thermostats/fire alarms, expansion joints in bridges and railways.
* Consequences: If not accounted for, expansion can cause damage (e.g., buckling railway tracks).
Supplement
3. Explanation (Particles):
* Heating → Particles gain kinetic energy → Vibrate/move more → Take up more space.
* Gases expand most because intermolecular forces are weakest, allowing particles to move apart easily.
##### 2.2.2 Specific Heat Capacity
Core
1. Internal Energy: A rise in temperature increases the internal energy (total kinetic and potential energy) of an object.
Supplement
2. Temperature & Kinetic Energy: A temperature increase corresponds to an increase in the average kinetic energy of all the particles.
3. Definition & Equation:
The *specific heat capacity (c)** is the energy required to raise the temperature of 1 kg of a substance by 1 °C.
* \( \Delta E = m c \Delta \theta \)
* Where:
* \( \Delta E \) = change in thermal energy (J)
* \( m \) = mass (kg)
* \( c \) = specific heat capacity (J/kg°C)
* \( \Delta \theta \) = change in temperature (°C)
4. Experiment to Measure c:
1. Find mass of substance, \( m \) (kg).
2. Measure initial temperature, \( \theta_1 \) (°C).
3. Supply a known amount of energy, \( \Delta E \) (J), using an immersion heater for a measured time, \( t \) (s). \( \Delta E = VIt \) or \( \Delta E = Pt \).
4. Stir and measure the final temperature, \( \theta_2 \) (°C).
5. Calculate \( \Delta \theta = \theta_2 - \theta_1 \).
6. Use \( c = \frac{\Delta E}{m \Delta \theta} \).
* Precautions: Insulate the container to minimize energy loss to surroundings.
##### 2.2.3 Melting, Boiling & Evaporation
Core
1. Energy without Temp Change: During melting/boiling, energy input is used to overcome intermolecular forces (increase potential energy), not to increase kinetic energy, so temperature remains constant.
2. Values for Water:
Melting point (at std. atm. pressure): *0 °C**
Boiling point (at std. atm. pressure): *100 °C**
3. Condensation & Solidification:
* Condensation (Gas→Liquid): Particles lose kinetic energy, move closer together until forces of attraction pull them into a liquid state.
* Solidification/Freezing (Liquid→Solid): Particles lose more energy, slow down, and arrange into a fixed, regular pattern.
4. Evaporation: The escape of more energetic particles from the surface of a liquid.
5. Evaporation causes cooling because the higher-energy particles leave, lowering the average kinetic energy (and thus temperature) of the remaining particles.
Supplement
6. Boiling vs. Evaporation:
| Feature | Boiling | Evaporation |
| :--- | :--- | :--- |
| Where | Throughout liquid | At surface only |
| Temperature | At boiling point only | At any temperature |
| Rate | Fast | Slow |
| Bubbles | Yes | No |
7. Factors Increasing Evaporation Rate:
* ↑ Temperature: More particles have enough energy to escape.
* ↑ Surface Area: More particles are at the surface.
* ↑ Air Movement (Draught): Removes vapour, preventing particles from returning to liquid.
8. Cooling by Evaporation: An object (e.g., skin) in contact with an evaporating liquid (e.g., sweat) supplies energy to the liquid to enable evaporation. This energy transfer away from the object cools it down.
Heating/Cooling Curve:
```plaintext
Temperature (θ)
^
| E (Gas) . . . . . . . . . . . ./
| / /
| D (Gas) / /
| / /
| / B (Solid+Liquid) / C (Liquid)
|------/---------------------/------------>
| / /
| A (Solid) / Time
+----------------------------------------->
```
* A→B: Solid heating up (temp ↑)
* B→C: Melting (temp constant) - Latent Heat of Fusion
* C→D: Liquid heating up (temp ↑)
* D→E: Boiling (temp constant) - Latent Heat of Vaporization
* E→F: Gas heating up (temp ↑)
---
#### 2.3 Transfer of Thermal Energy
##### 2.3.1 Conduction
Core
1. Experiment:
* Good Conductor (Metal): Rod with wax tabs. Heat one end. Wax melts quickly along the rod.
* Bad Conductor (Insulator): Wax does not melt far from the heat source.
Supplement
2. Mechanism:
* Non-Metals: Energy transferred by vibrations passed between particles in the lattice.
* Metals: Energy transferred very effectively by free (delocalised) electrons that move rapidly through the metal, colliding with ions and other electrons.
3. Why Gases/Liquids are Poor Conductors: Particles are further apart, so collisions are less frequent and energy transfer is slower.
4. Conductivity Spectrum: Materials exist on a spectrum from excellent conductors (metals) to good insulators (wood, plastic), with many in between.
##### 2.3.2 Convection
Core
1. Importance: Main method of thermal energy transfer in fluids (liquids and gases).
2. Explanation & Experiment:
* Mechanism: Heated fluid expands, becomes less dense, and rises. Cooler, denser fluid sinks to take its place. This cycle creates a convection current.
* Experiment: Beaker of water with potassium permanganate crystal at the bottom. Heat gently with Bunsen burner. Coloured streams of warm water rising are visible.
##### 2.3.3 Radiation
Core
1. Nature: Thermal energy transfer by infrared (IR) waves. A form of electromagnetic radiation.
2. Medium: Does not require a medium. Can travel through a vacuum (e.g., heat from the Sun).
3. Surface Effects:
* **Good Absorber/Emitter:** Dull, black surfaces.
* **Good Reflector/Poor Absorber:** Shiny, white surfaces.
Supplement
4.&5. Energy Balance:
Constant Temperature: *Rate of energy absorption = Rate of energy emission.**
Heating Up: *Rate of absorption > Rate of emission.**
Cooling Down: *Rate of absorption < Rate of emission.**
6. Earth's Temperature: Balanced by incoming solar (shortwave) radiation and outgoing Earth's (longwave, IR) radiation. Greenhouse gases absorb and re-emit outgoing IR, warming the atmosphere.
7.&8. Experiments:
* Emitters: Place same-temperature water in dull black and shiny silver cans. The dull black can cools faster ( thermometer shows temp drops quicker) as it is a better emitter of IR.
* Absorbers: Place thermometers under a heat lamp behind dull black and shiny silver shields. The thermometer behind the dull black shield shows a greater temperature rise as it is a better absorber of IR.
9. Rate of Emission: Increases if surface temperature increases or surface area increases.
##### 2.3.4 Consequences of Thermal Energy Transfer
Core
1. Basic Applications:
* (a) Kitchen Pan: Metal base (good conductor) for efficient heating. Plastic handle (good insulator) to prevent burns.
* (b) Room Heater: Placed near floor. Heats air, which rises (convection), setting up a current to circulate warm air around the room.
Supplement
2. Complex Applications:
* **(a) Fire:** Conduction through the solid fuel. Convection as hot air and smoke rise. Radiation of heat to surrounding people/objects.
* **(b) Car Radiator:** Conduction from hot water to metal fins. Convection as air is blown over the fins, carrying heat away. Radiation from the hot radiator surface.
---
### Key Equation Summary
| Concept | Equation | Variables |
| :--- | :--- | :--- |
| Temperature Conversion | \( T \,(\text{K}) = \theta \,(\text{°C}) + 273 \) | \( T \)= Kelvin, \( \theta \)= Celsius |
| Boyle's Law | \( p_1V_1 = p_2V_2 \) | \( p \)= pressure, \( V \)= volume |
| Specific Heat Capacity | \( \Delta E = m c \Delta \theta \) | \( \Delta E \)= energy (J), \( m \)= mass (kg),<br> \( c \)= shc (J/kg°C), \( \Delta \theta \)= temp change (°C) |
| Electrical Energy | \( \Delta E = VIt \) or \( \Delta E = Pt \) | \( V \)= volts, \( I \)= amps, \( t \)= time (s), \( P \)= power (W) |