Temperature and kinetic theory

Physics> Temperature and kinetic theory

According to the kinetic theory of gas, it acts as a huge number of tiny particles (molecules and atoms) that are in constant, random movement.

Learning challenge

• Characterize a gas using the kinetic theory of gases.

Key points

• The pressure is caused by the impact of molecules moving at different speeds through the Brownian motion.
• The temperature index of an ideal monatomic gas acts as a measure of the average index of kinetic energy and its atoms. In kinetic theory, it is expressed by the formula:
• An ideal gas model is used to combine temperature and mean translational kinetic energy in thermodynamic balance.

Terms

• An ideal gas is a hypothetical concept whose molecules do not come into contact, but undergo elastic shocks with each other and with the walls of the vessel.
• A degree of freedom is any coordinate whose minimum number is required to indicate the movement of a mechanical system.
• Brownian motion is a disordered movement of elements that occurs due to the fact that they are affected by individual molecules of a liquid.

Introduction

The molecular kinetic theory of gases characterizes them as a huge number of tiny particles (atoms and molecules) in constant random movement. At these speeds, they constantly collide with other particles and the walls of the vessel. Fundamentals of molecular kinetic theory depict macroscopic gas properties (temperature, pressure, volume) based on their composition and movement.

According to the theory, pressure is caused not by a static impact between molecules, but by the collision of particles moving at different speeds through Brownian motion. The temperature index of an ideal monatomic gas acts as a measure of the average kinetic energy.

Real gases do not always match the ideal model. Shown here is the size of helium atoms relative to their spacing on a 1950 atmosphere scale.

The ideal gas model is used by kinetic theory to relate the temperature index to the average translational kinetic energy of molecules under thermodynamic balance. In classical mechanics, translational energy looks like:

E_k = 0.5 mv² (m is the mass of a particle, v is its velocity). The distribution of velocities (denoting translational kinetic energies) of particles in a classical ideal gas is called the Maxwell-Boltzmann arrangement. In theory, its temperature is related to the average kinetic energy and the degree of freedom E_k:

(K is Boltzmann’s constant). We also derive the equation for an ideal gas from microscopic theory:

pV = nRT (R is the ideal gas constant, n is the number of moles).

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