Enter the temperature (it is converted to kelvin internally) and the mass of the particle into the calculator to determine the thermal velocity (RMS thermal speed).
Thermal Velocity Formula
The following equation is used to calculate the thermal velocity (root-mean-square thermal speed) for a particle in a Maxwell–Boltzmann distribution.
v_{rms}=\sqrt{\frac{3kT}{m}}- Where vrms is the RMS thermal speed (m/s)
- k is the Boltzmann constant (1.380649×10−23 J/K)
- T is the absolute temperature (K)
- m is the mass of one particle (kg)
To calculate the thermal velocity (RMS thermal speed), take the square root of three times the Boltzmann constant times the absolute temperature divided by the particle mass.
What is a Thermal Velocity?
Definition:
In this calculator, thermal velocity refers to the root-mean-square (RMS) thermal speed of a particle due to random thermal motion; it depends on the particle’s temperature and mass.
How to Calculate Thermal Velocity?
Example Problem:
The following example outlines the steps and information needed to calculate thermal velocity (RMS thermal speed).
First, determine the absolute temperature. In this example, the absolute temperature is found to be 300 K.
Next, determine the mass of one particle. For this problem, the mass is found to be 4.651734×10−26 kg (a nitrogen molecule, N2).
Finally, calculate the thermal velocity using the formula above:
vrms = SQRT ( 3 * k * T / m )
vrms = SQRT ( 3 * 1.380649×10−23 * 300 / (4.651734×10−26) )
vrms ≈ 516.8 m/s
FAQ
What is the Boltzmann constant and why is it important in calculating thermal velocity?
The Boltzmann constant (k) is a physical constant that relates the average kinetic energy of particles in a gas with the temperature of the gas. It is crucial in calculating thermal velocity because it provides a link between the macroscopic temperature (a measure of thermal energy) and the microscopic motion of particles, allowing for the calculation of the speed at which particles move due to thermal energy.
How does the mass of a particle affect its thermal velocity?
The mass of a particle inversely affects its thermal velocity, meaning that as the mass increases, the thermal velocity decreases. This relationship is evident in the thermal velocity formula, where the mass (m) is in the denominator. Lighter particles, therefore, move faster at a given temperature than heavier particles because they have less inertia to overcome when being propelled by thermal energy.
Can thermal velocity be applied to all states of matter, or is it specific to gases?
While the concept of thermal velocity is most commonly associated with gases, where particles move freely and their speeds can be directly related to temperature, it can also apply to particles in liquids and solids in a more complex manner. In liquids and solids, particles are not free to move as in gases; however, they do vibrate or oscillate around fixed positions. The average kinetic energy of these movements, which increases with temperature, can be thought of in terms of a form of thermal velocity, though the actual motion is not as straightforward as in gases.
