Thermal Velocity Calculator

Calculate the thermal velocity of particles in a gas based on temperature and molar mass

Input Parameters

Calculation Results

Calculation Formula

vth = √(8RT/πM)

Where:
vth = Thermal velocity
R = Universal gas constant (8.314 J/(mol·K))
T = Temperature in Kelvin
M = Molar mass in kg/mol

Thermal Velocity Calculator Usage Guide

Learn how to use the Thermal Velocity Calculator and understand its working principles

How to Use This Calculator

  1. Enter the temperature in Kelvin (K). For example, room temperature is approximately 298 K.
  2. Enter the molar mass of the gas in grams per mole (g/mol). This can be found on the periodic table for individual elements or calculated for molecules.
  3. Click the "Calculate" button to compute the thermal velocity.
  4. The result will be displayed in meters per second (m/s).

Understanding Thermal Velocity

Thermal velocity (or most probable speed) is the speed at which the largest number of gas molecules move in a gas at a given temperature. It's an important concept in statistical mechanics and thermodynamics.

Principle of Calculation

The calculator uses the formula:

vth = √(8RT/πM)

Where:

  • vth is the thermal velocity
  • R is the universal gas constant (8.314 J/(mol·K))
  • T is the temperature in Kelvin
  • M is the molar mass in kilograms per mole

Example Calculation

For example, to calculate the thermal velocity of nitrogen (N₂) at room temperature (298 K):

  • Temperature = 298 K
  • Molar mass of N₂ = 28 g/mol = 0.028 kg/mol
  • Thermal velocity = √(8 × 8.314 × 298 / (π × 0.028)) ≈ 431.6 m/s