What is the relationship between temperature speed and kinetic energy?

What is the relationship between temperature speed and kinetic energy?
Figure \(\PageIndex{1}\) (Credit: Courtesy of Danny Meyer/U.S. Air Force; Source: http://commons.wikimedia.org/wiki/File:Baseball_swing.jpg(opens in new window); License: Public Domain)

Kinetic energy is the energy of motion. Any object that is moving possesses kinetic energy. Baseball involves a great deal of kinetic energy. The pitcher throws a ball, imparting kinetic energy to the ball. When the batter swings, the motion of swinging creates kinetic energy in the bat. The collision of the bat with the ball changes the direction and speed of the ball, with the idea of kinetic energy being involved again.

As stated in the kinetic-molecular theory, the temperature of a substance is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the motion of the particles. This is registered as an increase in the temperature of the substance.

At any given temperature, not all of the particles of a sample of matter have the same kinetic energy. Instead, the particles display a wide range of kinetic energies. Most of the particles have a kinetic energy near the middle of the range. However, a small number of particles have kinetic energies a great deal lower or a great deal higher than the average (see figure below).

What is the relationship between temperature speed and kinetic energy?
Figure \(\PageIndex{2}\): A distribution of molecular kinetic energies as a function of temperature. The blue curve is for a low temperature, while the red curve is for a high temperature. (Credit: Christopher Auyeung; Source: CK-12 Foundation; License: CC BY-NC 3.0(opens in new window))

The blue curve in the figure above is for a sample of matter at a relatively low temperature, while the red curve is for a sample at a relatively high temperature. In both cases, most of the particles have intermediate kinetic energies, close to the average. Notice that as the temperature increases, the range of kinetic energies increases and the distribution curve "flattens out". At a given temperature, the particles of any substance have the same average kinetic energy.

As a sample of matter is continually cooled, the average kinetic energy of its particles decreases. Eventually, one would expect the particles to stop moving completely. Absolute zero is the temperature at which the motion of particles theoretically ceases. Absolute zero has never been attained in the laboratory, but temperatures on the order of \(1 \times 10^{-10} \: \text{K}\) have been achieved. The Kelvin temperature scale is the scale that is based on molecular motion, and so absolute zero is also called \(0 \: \text{K}\). The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of the substance. For example, the particles in a sample of hydrogen gas at \(200 \: \text{K}\) have twice the average kinetic energy as the particles in a hydrogen sample at \(100 \: \text{K}\).

What is the relationship between temperature speed and kinetic energy?
Figure \(\PageIndex{3}\): Helium gas liquefies at \(4 \: \text{K}\), or four degrees above absolute zero. Liquid helium is used as a coolant for large superconducting magnets, and must be stored in insulated metal canisters. (Credit: Michael Pereckas (Flickr: Beige Alert); Source: http://www.flickr.com/photos/beigephotos/5633215176/(opens in new window); License: CC by 2.0(opens in new window))

Summary

  • Kinetic energy is the energy of motion.
  • At a given temperature, individual particles of a substance have a range of kinetic energies.
  • The motion of particles theoretically ceases at absolute zero.

Review

  1. What is kinetic energy?
  2. If the temperature increases, will particles move faster or slower than they would at a lower temperature?
  3. What is absolute zero?

What is the relationship between temperature speed and kinetic energy?

LICENSED UNDER

What is the relationship between temperature speed and kinetic energy?

The key difference between kinetic energy and temperature is that kinetic energy refers to the property of a moving object, specifically the work needed to accelerate a body from its resting state, whereas temperature is the thermal energy present in all matter.

Kinetic energy and temperature are related terms because the kinetic energy of a system can change according to the temperature changes in that system. For example, increasing the temperature can increase the velocity of the moving particles in the system, thereby increasing the kinetic energy of that system.

CONTENTS

1. Overview and Key Difference
2. What is Kinetic Energy 
3. What is Temperature
4. Relationship – Kinetic Energy and Temperature
5. Kinetic Energy vs Temperature in Tabular Form
6. Summary

What is Kinetic Energy

The kinetic energy of an object is the energy that arises due to motion. It is the work we need to accelerate an object having a certain mass from its rest state to a particular velocity state. During the acceleration of the object, it gets kinetic energy and maintains it (at the same level) until the speed changes. In contrast, the object does the same amount of work during decelerating its speed from that particular velocity to the rest state.

The kinetic energy of a non-rotating object having a mass of “m” that is moving at a speed of “v” is as follows;

E = ½mv2

However, this equation is important when speed “v” is a very small value compared to the speed of light. The unit of measurement for kinetic energy is joule, but the English unit for the measurement of kinetic energy is “foot-pound”.

We can simply understand the kinetic energy using the example of a cyclist who uses the chemical energy provided by the food he consumes to accelerate a bicycle to a required speed. Thereafter, the cyclist needs to maintain this energy level without doing any further work (other than the energy required to overcome air resistance and friction).

What is Temperature?

Temperature is the thermal energy of matter. This term can explain the physical quantity of that system, expressing the hot or cold nature of that system. It is the source of the heat and flow of energy of an object which occurs upon contact with another object that is hotter or colder than itself. The common symbol for temperature is “T” and the SI unit for the measurement of temperature is K (Kelvin).

We can measure the temperature using a thermometer. Usually, a thermometer is calibrated using different temperature scales with various different reference points. The most common scale for temperature measurement is the Celsius scale, and there are other scales such as the Fahrenheit scale and the Kelvin scale.

In theory, the lowest possible temperature value for an object or a system is called absolute zero. At that point, we cannot extract any more thermal energy from a body. At the experimental state, we cannot approach this temperature value, but we can get close to that point.

Typically, the temperature is an important property to study in all fields of natural sciences such as physics, chemistry, Earth science, astronomy, medicine, biology, ecology, material science, metallurgy, mechanical engineering, and geography.

We can describe temperature as a quality of a state of a material, and we can name this property as a more abstract entity compared to any particular temperature scale that we are using to measure it. Some writers tend to name it as hotness.

What is the Relationship Between Kinetic Energy and Temperature?

Kinetic energy is directly proportional to the temperature applied. When the temperature of a system increases, the vibrations and collisions of molecules in that system increase; therefore, the kinetic energy increases.

What is the Difference Between Kinetic Energy and Temperature?

Kinetic energy and temperature are two related terms in physical chemistry. Increasing the temperature can increase the kinetic energy because the motion of particles increases when the temperature is increased. The key difference between kinetic energy and temperature is that kinetic energy refers to the property of a moving object and is the work needed to accelerate a body from its resting state, whereas temperature is the thermal energy present in all matter.

The following table summarizes the difference between kinetic energy and temperature.

Kinetic energy and temperature are two related terms in physical chemistry. Increasing the temperature can increase the kinetic energy because the motion of particles increases when the temperature is increased. The key difference between kinetic energy and temperature is that kinetic energy refers to the property of a moving object where it is the work needed to accelerate a body from its resting state, whereas temperature is the thermal energy present in all matter.

Reference:

1. “Kinetic Energy and Temperature.” Chemistry LibreTexts, Libretexts, 14 July 2020.

Image Courtesy:

1. “Wooden roller coaster txgi“ (CC BY-SA 3.0) via Commons Wikimedia
2. “Thermometer CF” By Gringer – (Public Domain) via Commons Wikimedia