What is the average kinetic energy of the particles in a substance

Chris

Ah, the humble thermometer. Whether we want to know if our holiday turkey is cooked or if we need concrete proof that we’re too sick to attend school, a thermometer is the exact scientific tool we need. But what, exactly, does a thermometer measure? In other words, what is temperature, really?

Brittny

Whether it’s solid, liquid, or gas, all matter is made up of atoms and molecules. These particles are constantly in motion. They collide with each other and with the walls of anything they are contained in. We quantify the motions of the particles by their kinetic energies.

In chemistry, we define the temperature of a substance as the average kinetic energy of all the atoms or molecules of that substance.

Not all of the particles of a substance have the same kinetic energy. At any given time, the kinetic energy of the particles can be represented by a distribution. Some atoms or molecules have a lot of kinetic energy and move very fast. Other atoms or molecules have a little kinetic energy and move very slowly. It is the average kinetic energy of the particles that thermometers measure and we record as the temperature.

One process that illustrates varying kinetic energies particularly well is evaporation. As you probably know, evaporation is a phase change where particles of a substance move from the liquid phase into the gas phase.

But have you ever wondered how a puddle of water can evaporate at room temperature? Keep that in mind—we’ll come back to that question in a bit.

Chris

When we think about a phase change from liquid to gas, we often think about adding thermal energy to a liquid by heating it up. When we do, the molecules of the liquid move faster and spread slightly farther apart, until they acquire enough energy to overcome the attractions they have for other molecules of the liquid and enter the gas phase.

Think about this: If someone asked you to turn a beaker full of water into water vapor, what would you do?

Being the brilliant young scientist that you are, you might put it on a hot plate and crank up the heat. Now you can kick back and relax until the hot plate transfers enough energy to get all the water molecules to transition from the liquid phase to the gas phase. In less science-y terms, you would boil the water.

Boiling is a special example of a liquid-to-gas phase change that occurs at a specific temperature called the boiling point, where the vapor pressure of the substance is equal to one atmosphere pressure. Boiling is usually carried out using a continuous input of energy from an external source (like a hot plate) to keep the temperature constant.

The obvious conclusion is this: If you continuously add thermal energy from a hot plate you can cause a phase change from liquid to gas.

But how can a puddle of water evaporate at room temperature?

When water evaporates at room temperature, some fast-moving, highly energetic molecules have enough energy to overcome the attractions that individual molecules have for one another and enter the gas phase. As these high-energy molecules leave the liquid phase, the average energy of the remaining liquid molecules is lowered, and their temperature decreases. This liquid is at a lower energy than its surroundings, so it absorbs energy from those surroundings. The cycle continues as the puddle slowly disappears.

Boiling is a faster process because the surroundings (the hot plate) heat the liquid to a higher temperature where more molecules have high energy, so vaporization is faster. The hot plate is hotter than the liquid, so thermal energy transfer is fast enough to keep the liquid temperature constant at the boiling temperature.

Evaporation can take place at any temperature because some of the molecules in a liquid—the ones at the higher end of the distribution—will always have enough energy to enter the gas phase. Chris

To sum up, temperature represents the average kinetic energy of the particles of substance. But it’s the spread of kinetic energies among the individual particles that explains why puddles dry up.

Have you ever ridden a roller coaster? At the top of the tracks, the roller coaster car does not have kinetic energy because it is at rest. As it goes down, its kinetic energy slowly increases with its speed. Similarly, when a person rides a bicycle, it possesses kinetic energy. As the bicycle's velocity increases, so does its kinetic energy. A running person, a speeding bullet all have kinetic energy.

Kinetic energy (K.E.) is the energy possessed by an object in motion. Now, let’s understand kinetic energy and its dependence on other factors like temperature in more detail.

What is the average kinetic energy of the particles in a substance
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KINETIC ENERGY AND TEMPERATURE

According to the kinetic-molecular hypothesis, a substance's temperature is proportional to the average kinetic energy of its particles. When a substance is heated, some of the energy absorbed is kept inside the particles, while another energy accelerates particle motion. This is manifested as a rise in the material's temperature.

When studying kinetic energy in gas molecules and its relationship with temperature, we generally define the term ‘average kinetic energy.

AVERAGE KINETIC ENERGY:

The average kinetic energy of a gas molecule is defined as the product of half of the mass of each gas molecule and the square of the RMS speed. Mathematically, it's as follows:

What is the average kinetic energy of the particles in a substance

m is the mass

vᵣₘₛ is the RMS velocity

K is the average kinetic energy

RELATION BETWEEN AVERAGE KINETIC ENERGY AND TEMPERATURE:

The temperature of a substance is directly proportional to the average kinetic energy of the substance particles. Because the mass of these particles is constant, the particles must move faster as the temperature rises.

Here’s a simple experiment to help you understand👇:

  • Take two beakers, one with hot water and another with cold water.
  • Add a few drops of any dye in both beakers.
  • We observe that the dye particles in hot water show faster movement than those in cold water. The particles in both the beakers move at different speeds; they have different kinetic energies.
  • We can conclude that the particles in the hotter body have a comparatively larger average K.E. than the colder one. In this way, the average K.E. of particles is indicated by their temperature.

We have seen the effect of increasing temperature on kinetic energy. Now let’s discuss the possibility of decreasing the temperature of the system and its effect on kinetic energy.

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The kinetic energy of a particle decreases as we lower the system's temperature. But imagine we keep decreasing the temperature and reach absolute zero. Then what happens to kinetic energy?

ABSOLUTE ZERO:

  • Absolute zero on the Celsius scale is −273.15℃. The Kelvin scale is based on absolute zero and starts at 0K.
  • Absolute zero is where the kinetic energy of the particles is zero. That means all the motion between particles will cease.

What is the average kinetic energy of the particles in a substance
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CONCLUSION:

  • Kinetic energy is the energy possessed by an object in motion.
  • The temperature of a substance is directly proportional to the average kinetic energy of the substance particles.
  • Absolute zero is where the kinetic energy of the particles is zero.

FAQs:

1. What happens at absolute zero?

At absolute zero, the thermodynamic system has the lowest temperature, and the K.E of the particles is zero.

2. What temperature is absolute zero in Fahrenheit?

Absolute zero corresponds to −459.67℉ in the Fahrenheit scale.

3. What is the lowest temperature achieved?

−273.144℃ is the lowest temperature that we achieved in the laboratory.

We hope you enjoyed studying this lesson and learned something cool about Average kinetic energy and Temperature! Join our Discord community to get any questions you may have answered and to engage with other students just like you! Don't forget to download our App to experience our fun VR classrooms - we promise, it makes studying much more fun! 😎

SOURCES:

Average Kinetic Energy and Temperature

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What is the average kinetic energy of the particles in a substance

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