Thermal Physics

2.1.1 States of matter

Changes of state

2.1.2 Particle model

All matter is made of tiny particles (atoms, molecules, ions and electrons). The properties of each state come from how the particles are arranged, how they move, and how strongly they attract each other.

Temperature and particle motion. The hotter a substance, the faster its particles move, so the more kinetic energy they have. There is a lowest possible temperature, absolute zero, $-273\ ^\circ\text{C}$ (or $0\ \text{K}$), where the particles have the least possible kinetic energy.

Gas pressure. A gas exerts a pressure because its particles collide with the walls of the container. Each collision gives the wall a tiny force, and many collisions every second give a steady force per unit area, which is the pressure.

A graph of $p$ against $V$ at constant temperature is a curve that falls as $V$ increases. A graph of $p$ against $\frac{1}{V}$ is a straight line through the origin.

$p_2 = \frac{p_1V_1}{V_2} = \frac{100 \times 600}{200} = 300\ \text{kPa}$

2.2.1 Thermal expansion of solids, liquids and gases

Solids, liquids and gases expand when they are heated, and contract when they are cooled.

In terms of particles. When a substance is heated, its particles vibrate or move faster and push each other further apart. The particles themselves do not get bigger. For the same temperature rise, gases expand the most, then liquids, then solids expand the least.

Everyday applications and consequences

• Gaps are left in railway lines and bridges so they do not buckle in hot weather.
• Overhead power cables sag more in hot weather.
• A thermostat uses a bimetallic strip: two metals joined together that expand by different amounts, so the strip bends when heated and switches a circuit off.

The liquid-in-glass thermometer

The liquid (mercury or coloured alcohol) expands when it is heated and rises up a narrow tube. Two fixed points define the scale: $0\ ^\circ\text{C}$ (melting ice) and $100\ ^\circ\text{C}$ (boiling water at standard atmospheric pressure). A thermometer is more sensitive if it has a larger bulb and a narrower tube, because a small expansion then makes the liquid move a long way.

The kelvin scale

$25 + 273 = 298\ \text{K} \qquad 300 - 273 = 27\ ^\circ\text{C}$

A change of $1\ \text{K}$ is the same size as a change of $1\ ^\circ\text{C}$.

2.2.2 Specific heat capacity

An increase in the temperature of an object increases its internal energy. In terms of particles, the average kinetic energy of all the particles increases.

The specific heat capacity is the energy needed to raise the temperature of $1\ \text{kg}$ of a substance by $1\ ^\circ\text{C}$. Water has a high value, $4200\ \text{J/(kg }^\circ\text{C)}$, which is why it takes a long time to heat up and is good for storing heat.

$\Delta E = mc\,\Delta\theta = 2.0 \times 4200 \times 30 = 252\,000\ \text{J}$

$c = \frac{9000}{0.50 \times 20} = 900\ \text{J/(kg }^\circ\text{C)}$

Experiment to measure the specific heat capacity of a solid.

1. Find the mass of a metal block with a balance.
2. Put an electric heater and a thermometer into holes in the block (add a drop of oil for good thermal contact) and wrap the block in insulation to reduce heat losses.
3. Record the starting temperature. Switch on the heater for a measured time. Record the final temperature.
4. Calculate the energy supplied: $E = VIt$ (or from a joulemeter). Then use $c = \dfrac{\Delta E}{m\,\Delta\theta}$.

For a liquid, do the same with the heater and thermometer in the liquid in an insulated container, using the mass of the liquid. Stir the liquid so the temperature is the same throughout. The value is too high if heat is lost to the surroundings, so insulate well.

2.2.3 Melting, boiling and evaporation

At standard atmospheric pressure, water melts at $0\ ^\circ\text{C}$ and boils at $100\ ^\circ\text{C}$.

During melting or boiling, the substance takes in energy but its temperature does not change. On a graph of temperature against time for a heated substance, these are the flat parts. The same is true in reverse when a substance solidifies or condenses: energy is given out while the temperature stays constant.

Latent heat is the energy needed to change the state of a substance without changing its temperature.

• When a solid melts, the energy is used to break the bonds between the particles so they can move past each other.
• When a liquid boils, the energy is used to separate the particles completely, against the forces between them.
• The kinetic energy of the particles does not change, so the temperature stays the same.

Boiling and evaporation

Evaporation in terms of particles. The particles in a liquid move at different speeds. The more energetic particles near the surface can escape from the liquid if they are moving fast enough to overcome the attraction of the others.

Evaporation is faster when:

• the temperature is higher,
• the surface area is larger,
• there is air movement (wind) over the surface, which carries away the escaped particles.

Evaporation causes cooling. The particles that escape are the ones with the most kinetic energy, so the average kinetic energy of those left behind falls. The liquid gets cooler. This is why sweating cools the body.

2.3.1 Conduction

Conduction is the transfer of thermal energy through a material without the material itself moving.

• In all solids, the particles vibrate. The hot end vibrates more, and this passes along the lattice from particle to particle.
• In metals, there are also free (delocalised) electrons that move through the metal. They gain energy at the hot end and carry it quickly by colliding with atoms. This is why metals are good conductors.

Gases and liquids are poor conductors because their particles are further apart. Materials that conduct badly, such as wood, plastic, wool and air, are insulators.

Experiment to compare conductors. Fix equal rods of different materials to a heated tank (or heat their ends equally). Stick a drawing pin on each rod with wax. The pin falls first from the best conductor, because heat travels along it fastest.

2.3.2 Convection

Convection is the transfer of thermal energy by the movement of a liquid or gas. It cannot happen in solids or in a vacuum.

1. The fluid is heated. Its particles move apart, so it expands and becomes less dense.
2. The warm, less dense fluid rises.
3. Cooler, denser fluid sinks to take its place.
4. This sets up a circulating convection current.

Experiment. Drop a crystal of potassium permanganate to the bottom of a beaker of water and heat the water just beside it. The purple streak rises over the heat, travels across the top and sinks on the other side, showing the current. Smoke in a box above a candle shows the same thing in air.

2.3.3 Radiation

Thermal radiation is infrared radiation, a type of electromagnetic wave. All objects emit it, and the hotter the object the more it emits. Radiation needs no medium: it can travel through a vacuum. This is how the Sun's energy reaches the Earth.

The rate at which an object emits radiation also increases with its surface temperature and its surface area.

Experiments

• Good and bad emitters. Fill identical cans (one painted dull black, one shiny, others white or rough) with hot water of the same temperature and measure how fast each cools. The dull black can cools fastest.
• Good and bad absorbers. Place two metal plates (one dull black, one shiny) the same distance from a heater, each with a ball bearing stuck on the back with wax. The wax on the dull black plate melts first, so the ball falls first.

2.3.4 Consequences of thermal energy transfer

• A cooking pan. The base is metal, a good conductor, so heat passes through quickly. The handle is plastic or wood, a good insulator, so it stays cool.
• Heating a room. A radiator warms the air next to it. The warm air rises by convection and cooler air flows in to be heated, so the whole room warms. This is why a radiator is placed low down.
• An infrared thermometer. It detects the infrared radiation emitted by an object and so measures its temperature without touching it.
• Thermal insulation. A vacuum flask has a double wall with a vacuum between them (stops conduction and convection), silvered surfaces (reduce radiation) and a stopper (reduces convection and evaporation). In buildings, loft insulation and cavity-wall insulation trap pockets of air, which is a poor conductor, and double glazing does the same.