a physical theory explaining the properties and behavior of matter through the motion and interaction of its smallest particles: atoms, molecules, and ions.
Formula for molecular concentration: n = N / V — ratio of number of molecules to volume
n — concentration of particles (molecules) per unit volume. It is used to calculate pressure and other macroscopic quantities in a gas.
Formula for ideal gas pressure: P = (1/3)·m·n·v²̄ — relation of pressure to mass, concentration, and mean square velocity of molecules
Gas pressure is explained by molecular collisions with the walls.
m — mass of one particle,
v²̄ — mean square velocity,
n — concentration.
This equation relates microscopic parameters to macroscopic pressure.
Formula for kinetic energy: K = (1/2)·m·v² — energy of motion of a particle with mass m and velocity v
This is the mechanical energy of translational motion of a single particle. v — instantaneous velocity of the molecule.
Formula for pressure through average kinetic energy: P = (2/3)·n·K̄
K̄ — average kinetic energy of a particle. This form shows that pressure is proportional to the energy of molecules.
Formula for average kinetic energy of molecules: K̄ = (3/2)·k·T — temperature is proportional to the average kinetic energy of particle motion
Temperature is proportional to the average kinetic energy of particle motion. k — Boltzmann constant. The formula is fundamental for connecting MKT with thermodynamics.
Formula for kinetic energy: W = (1/2)·m₀·v² — energy of motion of a particle with mass m₀ and velocity v
m₀ — mass of one molecule, v — instantaneous velocity. This is the basis for deriving pressure and average energy of a gas.
Formula for ideal gas pressure: p = (2/3)·n·W̄ — pressure is proportional to molecular concentration and their average kinetic energy
The pressure of an ideal gas is directly proportional to the average kinetic energy of its molecules. The formula is derived based on modeling the chaotic motion of molecules.
Formula for the relationship between average kinetic energy of molecules and temperature: W̄ = (3/2)·k·T
Gas temperature serves as a measure of the average kinetic energy of its molecules. This is a fundamental relationship between macro and micro parameters.
Formula for root-mean-square velocity of molecules: v = √(3RT / μ) — depends on temperature, gas constant, and molar mass
The formula allows finding the average velocity of molecules at a given temperature. μ — molar mass of the gas, R — universal gas constant.
Formula for ideal gas state: p·V = N·k·T = n·R·T — relationship between pressure, volume, temperature, number of particles, and amount of substance
Connects macroscopic gas parameters: pressure, volume, and temperature —
with micro parameters: number of particles N or amount of substance n.
The formula comes in two forms:
• Microscopic: pV = NkT
• Macroscopic: pV = nRT
Formula for ideal gas state via mass: p·V = (m / μ)·R·T — relationship between pressure, volume, and temperature with gas mass and molar mass
m — mass of the gas, μ — its molar mass. The formula is useful for calculations with a given mass of substance.
Formula for the relationship between the universal gas constant, Avogadro's number, and Boltzmann constant: R = NA·k
This relationship allows transitioning from micro parameters (via k) to macro forms (via R). NA — Avogadro's constant.
Formula for mean square velocity of molecules: v²̄ = (3·k·T) / m₀ — depends on temperature, Boltzmann constant, and mass of one molecule
Allows calculating the average kinetic activity of molecules at a given temperature. k — Boltzmann constant, m₀ — mass of one molecule.
Formula for effective (root-mean-square) velocity of molecules: vrms = √(v²̄) — square root of the mean square velocity
This is the square root of the mean square velocity. Used in calculations of pressure, momentum, heat flux. The higher the temperature — the higher vrms.
Formula for root-mean-square velocity of molecules: v = √(3·R·T / μ) — depends on temperature, universal gas constant, and molar mass
Shows the dependence of the average velocity on temperature and molar mass of the gas. Useful for calculations where μ — the molar mass of the substance — is given.