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Temperature and Kinetic Theory
Introduction
Physics Textbooks Boundless Physics Temperature and Kinetic Theory Introduction
Physics Textbooks Boundless Physics Temperature and Kinetic Theory
Physics Textbooks Boundless Physics
Physics Textbooks
Physics
Concept Version 9
Created by Boundless

Overview of Temperature and Kinetic Theory

The kinetic theory of gases describes a gas as a large number of small particles (atoms and molecules) in constant, random motion.

Learning Objective

  • Describe gas using the kinetic theory of gases


Key Points

    • The kinetic theory posits that pressure is due to collisions between molecules moving at different velocities through Brownian motion.
    • The temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms. In kinetic theory, it is related to its average kinetic energy per degree of freedom Ek via the equation: $\overline{E}_\text{k} = \begin{matrix} \frac 1 2 \end{matrix}$ kT.
    • The kinetic theory of gases uses the model of the ideal gas to relate temperature to the average translational kinetic energy of the molecules in a container of gas in thermodynamic equilibrium.

Terms

  • ideal gas

    A hypothetical gas whose molecules exhibit no interaction and undergo elastic collision with each other and with the walls of the container.

  • degree of freedom

    Any of the coordinates, a minimum number of which are needed to specify the motion of a mechanical system.

  • Brownian motion

    Random motion of particles suspended in a fluid, arising from those particles being struck by individual molecules of the fluid.


Full Text

Introduction to Temperature and Kinetic Theory

The kinetic theory of gases describes a gas as a large number of small particles (atoms or molecules), all of which are in constant, random motion. The rapidly moving particles constantly collide with each other, and with the walls of the container. Kinetic theory explains macroscopic properties of gases (such as pressure, temperature, and volume) by considering their molecular composition and motion. Essentially, the theory posits that pressure is due not to static repulsion between molecules (as was Isaac Newton's conjecture) but rather due to collisions between molecules moving at different velocities through Brownian motion. Also, the temperature of an ideal monatomic gas is a measure of the average kinetic energy of its atoms, as illustrated in .

Translational Motion of Helium

Real gases do not always behave according to the ideal model under certain conditions, such as high pressure. Here, the size of helium atoms relative to their spacing is shown to scale under 1950 atmospheres of pressure.

The kinetic theory of gases uses the model of the ideal gas to relate temperature to the average translational kinetic energy of the molecules in a container of gas in thermodynamic equilibrium . Classical mechanics defines the translational kinetic energy of a gas molecule as follows:

$E_\text{k} = \begin{matrix} \frac 1 2 \end{matrix} mv^2$,

where m is the particle mass and v its speed (the magnitude of its velocity). The distribution of the speeds (which determine the translational kinetic energies) of the particles in a classical ideal gas is called the Maxwell-Boltzmann distribution. In kinetic theory, the temperature of a classical ideal gas is related to its average kinetic energy per degree of freedom Ek via the equation:

$\overline{E}_\text{k} = \begin{matrix} \frac 1 2 \end{matrix} kT$ ,

(k: Boltzmann's constant). We will derive this relationship in the following atoms. We will also derive the ideal gas law:

$pV = nRT$,

(R: ideal gas constant, n: number of moles of gas) from a microscopic theory.

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