1.0 Thermal Expansion in Solids
Heat is a form of energy that flows from a body at a higher temperature to a body at a lower temperature. In Class 8, we dive deeper into the physical effects of this energy, specifically Thermal Expansion. When a substance is heated, its molecules vibrate more violently, causing the substance to take up more space.
Types of Expansion in Solids
Solids expand in all three dimensions, and we categorize them as follows:
- Linear Expansion: Increase in the length of a solid (e.g., a long metal rod).
- Superficial Expansion: Increase in the area of a solid (e.g., a metal plate).
- Cubical Expansion: Increase in the volume of a solid (e.g., a metal cube).
1.1 Coefficient of Linear Expansion
Different materials expand at different rates even when given the same amount of heat. This rate of expansion is determined by a constant called the Coefficient of Linear Expansion ($\alpha$).
Linear Expansion Formula
$$\Delta L = \alpha \times L_0 \times \Delta T$$
Where: $\Delta L$ = Change in length, $L_0$ = Original length, $\Delta T$ = Change in temperature.
1.2 Practical Consequences
- Railway Tracks: Small gaps are left between successive rails to allow for expansion during hot summers. Without these gaps, the tracks would buckle and cause accidents.
- Iron Rims: Wooden cart wheels are fitted with iron rims by heating the rim first. As the rim expands, it fits over the wheel, and upon cooling, it contracts to grip the wheel firmly.
- Telephone Wires: Wires are kept slightly sagging in summer so that when they contract in winter, they do not snap.
When boiling water is poured into a thick glass tumbler, it often cracks. This is because glass is a poor conductor of heat. The inner surface expands instantly while the outer surface remains cool, creating uneven expansion that shatters the glass.
A brass rod is 2 metres long at 20°C. If its temperature is increased to 70°C, find the increase in its length. ($\alpha$ for brass = $0.000019 / ^\circ C$)
Solution:
1. Original Length ($L_0$): $2\,m$
2. Change in Temp ($\Delta T$): $70 - 20 = 50\,^\circ C$
3. Coefficient ($\alpha$): $1.9 \times 10^{-5} / ^\circ C$
4. Formula: $\Delta L = L_0 \times \alpha \times \Delta T$
5. Calculation: $\Delta L = 2 \times 0.000019 \times 50 = 0.0019\,m = 1.9\,mm$.
Final Answer: The increase in length is $1.9\,mm$.
The Eiffel Tower can grow up to 15 centimetres taller during the summer! This is entirely due to the thermal expansion of the iron structure as it soaks up the sun's heat.
2.0 Thermal Expansion in Liquids
Liquids do not have a fixed shape; they take the shape of their container. Therefore, they only exhibit Cubical (Volume) Expansion. Unlike solids, liquids expand significantly more for the same rise in temperature because their intermolecular forces are weaker.
2.1 Real and Apparent Expansion
When we heat a liquid in a container, the container also expands. This leads to two types of observed expansion:
- Apparent Expansion: The observed expansion of the liquid without considering the expansion of the container.
- Real Expansion: The actual expansion of the liquid. It is always greater than the apparent expansion.
The Relation
$$Real\,Exp. = Apparent\,Exp. + Exp.\,of\,Container$$
2.2 Anomalous Expansion of Water
Most liquids expand on heating and contract on cooling. However, water shows a very strange behavior between $0^\circ C$ and $4^\circ C$. This is known as Anomalous Expansion.
The $4^\circ C$ Rule
- When water is heated from $0^\circ C$ to $4^\circ C$, it contracts (volume decreases).
- At $4^\circ C$, water has its minimum volume and maximum density ($1000\,kg/m^3$).
- Above $4^\circ C$, it behaves normally and expands.
This anomalous behavior is a gift of nature! In cold countries, when the temperature drops, the surface water reaches $4^\circ C$, becomes dense, and sinks. The freezing starts at the top, leaving a layer of liquid water at $4^\circ C$ at the bottom, allowing fish and plants to survive even when the lake is frozen over.
A glass bottle completely filled with water and tightly closed is kept in a freezer. Why does it burst?
Solution:
1. When water in the bottle cools below $4^\circ C$, it starts to expand due to anomalous expansion.
2. Upon freezing into ice at $0^\circ C$, the volume increases significantly.
3. Since the bottle is tightly closed and rigid, it cannot accommodate this increased volume.
4. The outward pressure exerted by the expanding ice causes the bottle to burst.
Because ice is less dense than water (due to expansion while freezing), icebergs float on the ocean. If water contracted upon freezing like other substances, ice would sink, and the oceans would eventually freeze from the bottom up!
3.0 Thermal Expansion in Gases
Gases exhibit the maximum thermal expansion compared to solids and liquids. This is because the intermolecular forces of attraction in gases are negligible, allowing the molecules to move apart freely when their kinetic energy increases due to heat.
3.1 Characteristics of Gas Expansion
- Gases expand uniformly in all directions.
- For a given rise in temperature, all gases expand by nearly the same amount (unlike solids and liquids which depend on the material).
- Gas expansion is significantly affected by pressure. To study thermal expansion in gases, we usually keep the pressure constant.
3.2 Comparison of Expansion
The degree of expansion varies vastly across the three states of matter. For the same rise in temperature:
| State | Relative Expansion | Reason |
|---|---|---|
| Solids | Least | Strong intermolecular forces keep particles tight. |
| Liquids | Moderate | Weak forces allow more movement than solids. |
| Gases | Most | Negligible forces allow maximum separation. |
Charles's Law (Intro)
At constant pressure, Volume ($V$) is directly proportional to Absolute Temperature ($T$).
$$V \propto T$$
During hot summer months, the air inside car or bicycle tyres expands. If the tyres are over-inflated, the increased pressure from the expanding gas can cause the tyre to burst. It is always recommended to keep the tyre pressure slightly lower in summer.
Why does a balloon kept in the sun burst after some time?
Solution:
1. When the balloon is kept in the sun, the air molecules inside absorb thermal energy.
2. The kinetic energy of the air molecules increases, leading to thermal expansion.
3. Since gases expand significantly, the volume of the air inside increases rapidly.
4. The thin rubber walls of the balloon cannot withstand the increased pressure and eventually snap.
Hot Air Balloons work on the principle of thermal expansion. When the air inside the balloon is heated, it expands and becomes less dense than the cool air outside, causing the balloon to rise!
4.0 Methods of Heat Transfer
Heat energy always moves from a region of higher temperature to a region of lower temperature. There are three distinct ways this transfer happens, depending on the medium involved: Conduction, Convection, and Radiation.
4.1 Conduction: Transfer through Solids
Conduction is the process of heat transfer in solids where energy is passed from molecule to molecule through vibrations, without the molecules actually leaving their fixed positions.
- Good Conductors: Materials that allow heat to pass easily (e.g., Copper, Iron, Aluminum).
- Bad Conductors (Insulators): Materials that do not allow heat to pass easily (e.g., Wood, Plastic, Glass, Air).
4.2 Convection: Transfer through Fluids
Convection is the process of heat transfer in liquids and gases where the molecules themselves move from hotter regions to colder regions, carrying heat with them. This creates Convection Currents.
Sea Breeze and Land Breeze
During the day, land heats up faster than the sea. Warm air over land rises, and cool air from the sea blows in to take its place (Sea Breeze). At night, the process reverses as land cools down faster (Land Breeze).
4.3 Radiation: Transfer through Vacuum
Radiation is the process of heat transfer that does not require any medium. Heat travels in the form of electromagnetic waves (Infrared rays). This is how the Sun's heat reaches the Earth through the vacuum of space.
| Feature | Conduction | Convection | Radiation |
|---|---|---|---|
| Medium | Solids required | Fluids (L/G) required | No medium required |
| Molecule Motion | Vibrate only | Actual movement | No molecule involvement |
| Speed | Slow | Moderate | Fastest (Speed of light) |
A Thermos flask minimizes all three types of heat transfer:
1. Vacuum between walls prevents conduction and convection.
2. Silvered walls reflect heat back, preventing radiation.
3. Insulating cap prevents heat loss through the top.
Why are cooking utensils provided with wooden or plastic handles?
Solution:
1. Metals are good conductors of heat, meaning the body of the utensil becomes very hot quickly.
2. Wood and plastic are insulators (poor conductors).
3. Heat from the utensil does not conduct easily into the handle.
4. This allows us to hold the utensil safely without burning our hands.
We wear woolen clothes in winter not because wool "generates" heat, but because it traps a layer of air between its fibers. Since air is a poor conductor, it prevents our body heat from escaping into the cold surroundings!