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7.1Particles, temperature and energy
Particles
As we look closer at matter, we discover ever-smaller structures. We find that compounds are made out of molecules, molecules are made out of atoms and atoms contain nuclei and electrons. Nuclei, in turn, contain protons and neutrons. Today it is believed that electrons do not have any substructure, but the nucleons (that is, protons and neutrons) are known to be made out of quarks. It is not known if the quarks themselves are made out of smaller particles. In thermal physics we are mostly interested in molecules, atoms and electrons â we do not need to consider any smaller structures.
In this course we will be interested in the vapour (gas), liquid and solid states of matter, Figure 7.1. (There are other exotic states of matter which we will not discuss in this course.)

Figure 7.1: The vapour (gas), liquid and solid states of matter.

There are strong forces between particles in a solid which explains, for example, why it is difficult to break a solid apart. In liquids, the forces between the particles are weaker so particles are able to move around each other; this explains why a liquid flows and will take the shape of the container in which it is placed. However, the forces between particles in a liquid are sufficiently strong that the particles cannot move far from each other. Like solids, liquids are very nearly incompressible which suggests that the distances between the particles are similar to those in solids. In gases the forces between particles are very weak so they are essentially negligible. The only time significant forces exist between the particles is during collisions. Gases are very compressible, which is evidence that the distances between particles are large. Typically, distances between particles in gases are 10 times larger than those in solids and liquids.
This means that solids, liquids and gases also differ in density. Density, Ï, is the ratio of mass to volume (Ï=MV) and is measured in kg mâ3. Solid iron has a density of 7.8 Ã 103 kg mâ3 whereas liquid iron has a density that is somewhat less, 6.9 Ã 103 kg mâ3. Gases have a much lower density: air, for example, has a density of 1.2 kg mâ3 (but this depends on pressure and temperature as we will see). So solid and liquid densities are comparable, but gas densities are about 1000 times smaller.
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Temperature
We have an intuitive concept of temperature as the âcoldnessâ or âhotnessâ of a body, but it wasnât until the nineteenth century that one of the greatest discoveries in physics related the concept of temperature to the random motion of molecules. This connection, which we will explore in greater detail in ChapterÂ 9, is expressed as:
KEY POINT
Temperature (in kelvin) is proportional to the average random kinetic energy of the molecules, EÂ¯K
In equation form:
EÂ¯K=32kBT
In this equation kB = 1.38 Ã 10â23 J Kâ1 is a new constant in physics called the Boltzmann constant. We will work with this constant extensively in ChapterÂ 9.
This direct proportionality between temperature and the average random kinetic energy is only true for the absolute or kelvin temperature scale. In this scale, zero is the lowest possible temperature, the absolute zero of temperature. Since the lowest possible value of kinetic energy is zero the lowest possible value of temperature must also be zero as EÂ¯K and T are proportional.
Many other temperature scales exist. In 1742, Anders Celsius (1701â1744) created the temperature scale that is still commonly used today and is known by his name. On the Celsius scale a value of zero degrees is assigned to the freezing point of water and a value of 100 degrees is assigned to the boiling point of water. The connection between the Celsius and Kelvin scales is:
T(in kelvin,Â K)=T(in degrees Celsius,Â Â°C)+273
The lowest possible temperature on the absolute scale is zero kelvin, 0 K. On the Celsius scale the lowest possible temperature is, therefore, â273 Â°C.
Temperature has varied a lot in the life of the universe: at the time of the Big Bang, some 13.8 billion years ago, the temperature of the universe was about 1032 K. The universe has been expanding ever since, and so the temperature has been dropping. In the emptiness of space, far from stars and galaxies, its value today is only 2.7 K, Figure 7.2.

Figure 7.2: The top image shows the variation of temperature in the entire observable universe. Different colours represent tiny fluctuations about the average temperature of 2.7 K. On an entirely different scale, the lower image shows variations of the average surface temperature of the earth in January for the period Â­1961â1990.

EXAM TIP
The magnitude of a kelvin is the same as that of a degree Celsius.
The need to agree on internationally accepted units, among them those for temperature, is a good example of international collaboration to establish international systems of measurement.
CHECK YOURSELF 1
aWhat is 300 K in degrees Celsius?
bWhat is â150 degrees Celsius in kelvin?
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WORKED EXAMPLE 7.1
The temperature of a body increases from 320 K to 340 K. State the temperature increase in degrees Celsius.
Answer
The temperature increase in kelvin is 340 â 320 = 20 K.
Since the magnitude of a kelvin is the same as that of a degree Celsius, the temperature increase is 20 Â°C.
(Another way to look at this is to convert both temperatures to kelvin. 320 K corresponds to 320 â 273 = 47 Â°C and 340 K corresponds to 340 â 273 = 67 Â°C, giving a change of 20 Â°C.)
Thermal energy (heat)
When two bodies are in contact and have different temperatures, there will be a transfer of thermal energy from the hotter to the colder body. So, when a glass of cold water is placed in a warm room, thermal energy transfers from the room into the colder water until the temperature of the water becomes equal to that of its surroundings; thermal equilibrium has been reached. We say that the colder body has been âheatedâ.
In other words, thermal energy is the energy that gets transferred from one body to another as a result of a temperature difference. The term heat is also used.
Internal energy
We know that there are forces between particles. For gases, these forces are very smallâunder reasonable conditions (low density) they are almost negligible. But forces between particles are substantial for solids. In a solid the forces between the particles can be modelled by springs joining neighbouring particles, Figure 7.3. The springs represent the bonds between the particles.

Figure 7.3: Particles in the solid phase oscillate about fixed positions but are not free to move inside the solid.

Just as we need to do work to stretch an ordinary spring (this work increases the elastic potential energy of the spring) we need to do work to increase the separation of the particles in a solid. This work goes into a new form of energy: intermolecular potential energy.
Figure 7.4 shows the intermolecular potential energy EP of one pair of molecules as a function of the distance r separating the two molecules in a solid.
THEORY OF KNOWLEDGE
Heat was once thought to be a fluid (called âcaloricâ) that moved from body to body. The more caloric a body contained the hotter it was, and as caloric left a body the body became colder. But you can warm your hands by rubbing them together. If caloric entered your hands it must have come from another body, making it colder. But this does not happen, and so the caloric theory must be false. In the nineteenth century heat was shown to be just another form of energy.
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Figure 7.4: The average separation of the two molecules is the separation at the minimum of the curve, i.e. at approximately 1.2 nm.

The average separation of the molecules corresponds to the minimum of the curve, about 1.2 nm for this graph. For separations larger than 1.2 nm the forces between molecules are attractive. For smaller separations, the forces are repulsive, indicating that the molecules cannot get that close to each other. Notice also that this potential energy is negative (for separations larger than 1 nm). For a gas, the potential energy is zero. This means that in going from a solid to a liquid and then a gas, the potential energy increases.
KEY POINT
We define the internal energy of a substance as:
the total random kinetic energy of the particles of a substance, plus the total intermolecular potential energy of the particles: U = total random kinetic energy + total intermolecular potential energy.
CHECK YOURSELF 2
Two identical containers are filled with the same quantity of gas at the same pressure and temperature. One container is at rest in a laboratory, and the other is on board a fast aircraft. A student says that the internal energy of the gas in the container on the aircraft is larger. Comment on this statement.
Energy transferred from a hot to a cold body increases the internal energy of the cold body (and decreases the internal energy of the hot body by the same amount).
The internal energy of a system can change as a result of thermal energy added or taken out but also as a result of work performed. This connection between internal energy, thermal energy and work will be explored in detail in ChapterÂ 10.
Internal energy, thermal energy and work are three different concepts. What they have in common is that they are all measured in joules. Temperature is a measure of the random kinetic energy of a substanceânot its internal energy.
TEST YOUR UNDERSTANDING
1Explain why molecular motion stops at absolute zero. Calculate the average kinetic energy of molecules kept at 300 K.
2Helium and neon are kept at the same temperature. How does the average kinetic energy of helium compare with that of neon? Do the molecules of neon move as fast as those of helium?
3Distinguish between internal energy and heat.
4A student says that a body at high temperature has more internal energy than a body at a lower temperature. What is wrong with this statement?
5Metals expand when heated. Based on this fact, state one change to the graph of Figure 7.4 when the temperature increases.
6Does the density of a block of copper depend on the size of the block? Does it depend on the mass of the block?
7The density of copper is 8.9 Ã 103 kg mâ3 and its molar mass is 64 g molâ1. Estimate the centre-to-centre separation of two copper atoms listing the assumptions you make.
