# Thermal concepts

Imagine sliding a heavy object across a room. You feel slightly more tired because you have done work against friction and the object gains speed. But what about when you finish? Where has the energy gone?

To understand what happens, we need to look inside the object. Having studied mechanics, which is basically the physics of a small ball, you will be ready to apply what you know the the small particles that make up matter, atoms and molecules.

Key Concepts

Kinetic theory

Atoms and molecules

Atoms and molecules are types of particle and are the smallest parts of matter.

• Elements from the Periodic Table (e.g. aluminium, argon) are made of atoms
• A molecule is two or more atoms chemically bonded together. Some of these are elements (e.g. oxygen) but some are compounds (e.g. water, methane).

In this topic we will usually assume that the atoms or molecules are uncharged and do not interact, like a large number of very small perfectly elastic balls. (For a more truthful account, study chemistry!)

States of matter

We will assume that all substances are either a solid, liquid or gas (or possibly a combination, like melting ice). There are other states of matter, but these extend far beyond your subject guide!

Solid: Fixed shape and volume since atoms are held together in rows

Liquid: No fixed shape but fixed volume since atoms are held together, but can move relative to each other

Gas: No fixed shape or volume since atoms are free to move. A gas will fill its container by diffusion.

Brownian motion

In the early 19th century, Robert Brown noticed that visible pollen grains (like the large green sphere) moved about on the surface of water. He deduced that the water was made of particles too small to be visible to the eye (like the small green spheres).

Brownian motion also explains the random motion of smoke particles knocked about by gas atoms.

Relative atomic (or molecular) mass, $$M_r$$

The unit of atomic mass is based on the mass of a carbon-12 atom.

1 u is $$1\over12$$th of the mass of a carbon-12 atom

The simplest way to explain this is that the hydrogen is the smallest atom and has a mass of approximately 1 u. Carbon-12 has a mass of exactly 12 u.

NB: Not all atoms have the $$M_r$$ shown on the Periodic Table. Carbon-14 also exists and is known as an isotope of carbon (same number of protons but different number of neutrons).

Avogadro's constant, $$N_A$$

Just as we know that a pair means 2 and a dozen means 12, Avogadro's constant is a number. It is useful for measuring the amount of a substance.

$$N_A$$ is the number of atoms in 12 g of carbon 12 = 6.02 x 1023

Moles, $$n$$

As you can anticipate, stating the number of particles in an object could be cumbersome because of the very large numbers involved. Instead, we can calculate the number of moles.

A mole is an Avagadro's constant of particles:

$$n={N\over N_A}$$

It is a dimensionless quantity, but it is conventional to write 'moles' after the number in your answer.

Essentials

Microscopic terms

Heat and temperature

Heat and temperature are used interchangeably in everyday language. However, they have different definitions in physics.

Heat is the total quantity of energy in a body (sort of like adding up the kinetic energy of every particle inside).

When two bodies are in thermal contact, heat will flow from the hot one to the cold one until they are the same temperature. The bodies are then said to be in thermal equilibrium.

Unit: Joule (J)

Temperature is a measure of how hot or cold a body is. The temperature of a body is related to the average kinetic energy of the molecules.

If heat is the overall energy, temperature acts as a measure of 'energy density'.

Unit: °C or K  (0°C = 273 K)

A lit match has a much higher temperature than ice, but an ice berg has more energy overall.

One analogy you could try at home is to add juice to water. You could pour a full glass of juice (lots of energy) into a bath of water and not notice much colour change in the water after stirring (low temperature). However, a glass that is half water and half juice (less energy) will appear orange (high temperature).

Internal energy

The internal energy of a substance is the sum of the kinetic and potential energies of all the particles:

$$U=\Sigma E_k+\Sigma E_p$$

In IB Physics we make the assumption that there is no force between the atoms of a gas. This means that they have no potential energy. Therefore, internal energy is the sum of the kinetic energies (but you must memorise the definition in green!).

Is this a good assumption?

Generally, yes. The masses of molecules are so small that it is reasonable to ignore gravitational potential energy. Molecules in the air and ideal gas atoms also have no overall charge, so electric potential energy can be ignored.

#### Summary for an ideal gas

Temperature: Average Ek
Internal energy: Sum of Ek
Heat: Is transferred to change temperature

Macroscopic terms

Mechanisms for heat transfer

Conduction is the transfer of heat by molecules vibrating and colliding to pass Ek from one to another. This is common in solids (particles close together) and is fast in metals (electrons free to move). A poor conductor of heat is called an insulator.

Convection is the transfer of heat due to changes in density of fluids (liquids and gases). In this process the actual hot liquid/gas moves about as a whole (rather than individual particles).

Radiation is the transfer of heat by all hot objects by electromagnetic waves (infra red). Radiation can travel through any substance or vacuum. Black objects both radiate and absorb better than light coloured objects.
The amount of radiation (power per unit area) increases with increased temperature.

Evaporation is the transfer of heat when particles of higher energy in a liquid join the surrounding air, leaving particles of lower average energy behind.

Heat changes

#### Thermal capacity

When heat is added to a body, its temperature increases proportionally (provided there is no change of state). The constant of proportionality is the thermal capacity of the body.

Thermal capacity is the amount of heat required to raise the temperature of a body by 1 K = $$Q\over \Delta T$$

Unit: JK-1

You might notice that this is not a particularly useful quantity to measure as it would only apply to an exact amount of an exact substance, and so could not be used by more than one scientific researcher. Instead, it is preferable to measure a material property (where the quantity is irrelevant)...

#### Specific heat capacity, $$c$$

Specific heat capacity relates the temperature change to heat transferred for a specific material. When a material changes temperature due to a change in heat, we call this "sensible heat".

Specific heat capacity is the amount of heat required to raise the temperature of 1 kg of material by 1 K.

$$c= {Q\over m\Delta T}$$

Unit: Jkg-1K-1

For referece, the specific heat capacity of water is approximately 4200 Jkg-1K-1.

The term "specific" in physics means "divide by mass". In chemistry, you might have heard that the specific heat capacity of water is "4.2", because chemists tend to work in grams rather than kilograms.

#### Specific latent heat, $$L$$

When a material changes state due to a change in heat, we call this "latent heat".

Specific latent heat is the amount of heat required to change the state of 1kg of a substance without changing its temperature:

$$L={Q\over m}$$

Unit: Jkg-1

We assume that it is not possible to increase the temperature of a substance by heating until a state change has been completed. For example, water would remain at 0 oC until all ice has melted.

Test Yourself

Use flashcards to practise your recall.

Just for Fun

Check out this πg physics summary.