Thermal Physics Notes

9.1 Thermal Expansion

Materials expand when heated and contract when cooled. The amount of expansion or contraction depends on the material and the temperature change.

• Solids: Expand the least; expansion often not visible.

• Liquids: Expand more than solids.

• Gases: Expand the most.

Expansion of a Metal

Figure 9.1 shows a metal ball that fits through a ring at room temperature. When heated, the ball expands and no longer fits through the ring.

Expansion of a Liquid in a Thermometer

Figure 9.2 shows a liquid-in-glass thermometer. When the bulb is heated, the liquid expands and rises in the capillary tube.

Expansion of Gases

Gases expand much more than liquids. Figure 9.3 shows air in a test tube expanding when warmed by hands, causing bubbles to escape.

Why Different Amounts?

Heating increases the kinetic energy of particles.

• Solids: Particles vibrate more vigorously; strong forces result in small expansion.

• Liquids: Particles move faster; weaker forces lead to greater expansion.

• Gases: Particles move fastest; very little force between particles results in the greatest expansion.

When heated, the volume that particles occupy increases; the particles themselves do not expand (Figure 9.4).

Applications and Consequences of Expansion

Engineers must consider expansion when designing structures to accommodate large forces.

Railway Lines

Some railway lines have expansion gaps (Figure 9.5) to allow for expansion in hot weather.
Modern railway lines are designed to fit tightly on a hot day and are held in place by supporting structures to manage contraction on cold days.

Bridges

Bridges also expand and contract. Expansion gaps (Figure 9.6) or rollers (Figure 9.7) accommodate this.

Shrink Fitting

Expansion can be used to join metal parts. For example, a metal axle can be fitted into a metal train wheel (Figure 9.8). The axle is cooled to shrink it so it fits into the wheel. When it warms up, it expands and the parts are held firmly together.

According to K.P.M., particles in solids vibrate about fixed positions. When cooled, particles lose energy and vibrate less, resulting in contraction.

Wires expand on hot days due to thermal expansion and hang more loosely.

9.2 Specific Heat Capacity

Internal Energy

Internal energy is the total energy of all particles in a substance. It exists when the temperature is above 0 Kelvin. Thermal energy transferred to a substance increases its internal energy because the particles gain kinetic energy, making the substance hotter.

• Greater the temperature = greater the internal energy.

Units: J (Joules)

Thermal energy from a flame increases the water's internal energy (Figure 9.9).

Temperature measures the average kinetic energy of particles; higher temperature means greater internal energy (Figure 9.10).

Specific Heat Capacity

Specific heat capacity ($c$$$c$$) is the amount of thermal energy required to raise the temperature of a unit mass (e.g., 1 kg) of a substance by 1°C (or 1 K).

• Thermal energy needed depends on: Mass of water, temperature change, and the type of material.

$c = \frac{\Delta E}{m \Delta \theta}$$$c = \frac{\Delta E}{m \Delta \theta}$$

Where:

• $\Delta E$$$\Delta E$$ = Thermal energy required (in J)

• $m$$$m$$ = Mass of substance (in kg)

• $\Delta \theta$$$\Delta \theta$$ = Temperature change (in °C or K)

Units for specific heat capacity: J/(kg°C) or J/(kg K)

The equation can be rearranged as: $\Delta E = mc \Delta \theta$$$\Delta E = mc \Delta \theta$$

Water has a high specific heat capacity (4200 J/(kg°C)), meaning it takes 4200 J of energy to raise the temperature of 1 kg of water by 1°C.

Table 9.1 provides specific heat capacities of common materials.

Worked Example 9A

Calculate the temperature change of 1 kg of copper when it is supplied with 4200 J of thermal energy.

Solution

Using $\Delta E = mc \Delta \theta$$$\Delta E = mc \Delta \theta$$:

$4200 = 1 \times 400 \times \Delta \theta$$$4200 = 1 \times 400 \times \Delta \theta$$

$\Delta \theta = 10.5°C$$$\Delta \theta = 10.5°C$$

9.3 Changes of State

Melting occurs when a solid changes to a liquid upon heating. Boiling occurs when a liquid changes to a gas upon heating.

Experiment: Heat crushed ice and record the temperature every minute until the melted ice boils (Figure 9.13).

Figure 9.14 shows a graph of temperature against time.

• A to B: The temperature of the ice rises from -10°C to 0°C. Thermal energy increases the temperature.

• B to C: The temperature remains constant at 0°C. Thermal energy is used for melting (solid + liquid).

• C to D: The temperature rises from 0°C to 100°C. Thermal energy increases the temperature of the liquid water.

• D to E: The temperature remains constant at 100°C. Thermal energy is used for boiling (liquid + gas).

Energy and Changes of State

During melting, energy is needed to break the bonds holding particles in fixed positions. Melting occurs at the melting point without a temperature change. The melting point of pure water is 0°C at standard atmospheric pressure.

During boiling, energy is needed to break the bonds between particles in a liquid and to overcome atmospheric pressure. Boiling occurs at the boiling point without a temperature change. The boiling point of pure water is 100°C at standard atmospheric pressure.

During condensation (gas to liquid), forces pull particles closer, and energy is released.

During solidification (freezing, liquid to solid), strong forces pull particles into fixed positions, and energy is released.

Figure 9.15 shows the changes of state as matter loses heat.

At higher altitudes, water boils at a lower temperature because atmospheric pressure is lower.

Burns from steam are more painful than burns from hot water because steam releases more thermal energy upon condensing.

Evaporation

Evaporation is the change of state from liquid to gas.

The kinetic theory of matter explains how evaporation occurs (Figure 9.16):

1. Molecules in a liquid move randomly at different speeds (different kinetic energies).

2. At the surface, molecules with enough energy overcome attractive forces and atmospheric pressure to escape into the atmosphere.

3. Less energetic molecules are left behind, decreasing the average kinetic energy (and therefore temperature) of the liquid.

Evaporation causes cooling.

Stepping out of a pool on a windy day feels cold because water evaporates from the skin surface, resulting in a decrease in temperature (Figure 9.17).

On a hot day, sweat evaporates from the skin. Water molecules with enough kinetic energy escape, overcoming attractive forces and atmospheric pressure. The fastest-moving molecules leave, reducing the average kinetic energy and thus the temperature. Evaporated water molecules carry away body heat, cooling the body.

Table 9.2 outlines the differences between boiling and evaporation:

Factors affecting the rate of evaporation (Figure 9.19):

• Temperature: Higher temperature increases the rate of evaporation; more surface molecules have enough energy to escape.

• Surface Area: Larger surface area increases the rate of evaporation; more molecules can escape.

• Movement of Air: Moving air removes escaped molecules, maintaining drier air and increasing evaporation rate.