Microscopic View of Temperature

Syllabus Content:

Kelvin temperature is a measure of the average kinetic energy of particles as given by Ek = 3/2kBT
The internal energy of a system is the total intermolecular potential energy arising from the forces between the molecules plus the total random kinetic energy of the molecules arising from their random motion

Internal Energy:

From a macroscopic view, we often think of temperature as a measure of how "hot" or "cold" a substance is. However, in the kinetic theory of matter, we view temperature as a relationship to the average kinetic energy of the particles in the substance.

The internal energy of a system refers to the total intermolecular potential energy arising from the forces between the molecules, plus the total random kinetic energy of the molecules arising from their random motion.

Kinetic Energy of Particles:

The kinetic theory of matter states that all matter is composed of tiny particles called atoms or molecules that are constantly in motion. These particles possess kinetic energy, which can be classified into different types depending on the nature of their motion.

Vibrational Kinetic Energy:

In solids, particles are closely packed and have limited freedom of movement. However, they can still vibrate about their equilibrium positions. This vibration gives rise to vibrational kinetic energy. Consider a solid material such as a metal rod. When the rod is heated, the increased temperature causes the atoms to vibrate more vigorously, leading to an increase in vibrational kinetic energy.

Translational Kinetic Energy:

In liquids and gases, particles have more freedom of movement compared to solids. They can move from one location to another, leading to translational kinetic energy. For example, imagine a glass of water. The water molecules are constantly moving and colliding with each other, possessing translational kinetic energy. When the water is heated, the average translational kinetic energy of the molecules increases.

Rotational Kinetic Energy:

In addition to vibrational and translational motion, particles can also rotate about their axes. This rotational motion contributes to rotational kinetic energy. Consider a gas molecule in a container. As the temperature of the gas increases, the molecules move with higher speeds, leading to an increase in both translational and rotational kinetic energy.

Kinetic Energy & Tempeature:

Heating water on a stove transfers the heat (thermal) energy of the flame to the kinetic energies of the molecules. As the temperature increases so does the kinetic energy.

Temperature is a measure of the average kinetic energy of particles in a substance. It provides information about the motion of particles at the microscopic level. To understand this concept, let's consider a gas in a container.

In a gas, the molecules are constantly moving and colliding with each other. Each molecule has its own kinetic energy, as some molecules move faster while others move slower. The temperature of the gas is a measure of the average kinetic energy of all the gas molecules.

When the temperature of a substance increases, the average kinetic energy of the particles also increases. This implies that the particles are moving faster on average. Conversely, when the temperature decreases, the average kinetic energy decreases, and the particles move slower on average.

Colder objects have particles than move slower and have less translational energy than hotter objects.

Kelvin Scale & Temperature:

When relating temperature to the average kinetic energy of a substance, it is crucial to use the Kelvin temperature scale. The Kelvin scale is an absolute temperature scale where zero Kelvin (0 K) represents the absence of any thermal energy. In contrast, the Celsius scale uses the freezing point of water as its zero point.

The Kelvin temperature scale allows us to directly relate temperature to the average kinetic energy of particles. At absolute zero (0 K), particles have minimal kinetic energy, and as the temperature increases, the average kinetic energy of the particles also increases.

Many IB students make the mistake of using Celsius when computing the average kinetic energy. Only the Kelvin scale is an absolute scale. The IB exam will often give students the temperature in Celsius, and you will need to convert to Kelvin before performing any calculations involving energy.

Potential Energy of Particles:

Potential Energy in Solids and Liquids:

Particles, especially those in solids and liquids, can also possess potential energy due to the intermolecular forces between them. These forces arise from the electrical interactions between particles and determine the arrangement and behavior of particles in a substance.

When the separation between particles in a solid or liquid increases, the potential energy of the system also increases. For example, when a solid is heated, the particles gain energy, leading to an increase in separation and potential energy. This increase in potential energy contributes to the overall internal energy of the substance. We'll revisit this concept when we discuss phase changes.

Intermolecular Forces in Gases:

Unlike solids and liquids, the intermolecular forces between molecules in gases are often negligible. In gases, the particles are typically far apart and the forces of attraction between them are weak. Consequently, the potential energy contribution to the internal energy of a gas is relatively small compared to the kinetic energy of the particles.

For example, consider a gas in a container. The main component of the internal energy of the gas arises from the random motion of the molecules, which contributes to their kinetic energy. The potential energy arising from intermolecular forces is usually considered negligible in gases.

Summary:

The internal energy of a substance is a combination of both kinetic and potential energies. The kinetic energy is associated with the motion of particles (vibrational, translational, and rotational), while the potential energy arises from the intermolecular forces between particles.

Temperature is a measure of the average kinetic energy of the particles, and it is only related to the Kelvin temperature scale. The intermolecular forces between particles play a role in determining the internal energy, especially in solids and liquids. In gases, these forces are usually negligible compared to the kinetic energy of the particles.

Comprehesion Questions:

Define internal energy
How does heating a liquid affect the average translational kinetic energy of its molecules?
What is the relationship between temperature and the average kinetic energy of particles in a substance?
Why should the Kelvin temperature scale be used when relating temperature to average kinetic energy?
Why is the potential energy contribution to the internal energy of a gas considered negligible?

Comprehension Questions Answers:

Define internal energy

The internal energy of a system consists of the total intermolecular potential energy arising from the forces between the molecules and the total random kinetic energy of the molecules arising from their random motion

How does heating a liquid affect the average translational kinetic energy of its molecules?

Heating a liquid increases the average translational kinetic energy of its molecules.

What is the relationship between temperature and the average kinetic energy of particles in a substance?

The average kinetic energy of particles in a substance increases with an increase in temperature and decreases with a decrease in temperature.

Why should the Kelvin temperature scale be used when relating temperature to average kinetic energy?

The Kelvin temperature scale is important when relating temperature to average kinetic energy because it is an absolute temperature scale where zero Kelvin represents the absence of any thermal energy and the point at which all molecular motion stops.

Why is the potential energy contribution to the internal energy of a gas considered negligible?

The increased distance between particles in gasses lead to very weak intermolecular forces which makes the total potential energy much less than the kinetic energy of the gas particles which are moving at high speeds.

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