# Thermal Velocity

What is thermal velocity? What is it's physical significance? Wikipedia says:

The thermal velocity or thermal speed is a typical velocity of the thermal motion of particles which make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature.

But I cannot understand and comprehend it.

• Which parts of the explanation are giving you trouble? As it stands, you're likely to get another explanation very similar to the one you've already read as an answer, which won't be very helpful. If you can be specific about which part you didn't understand, you may get more useful answers. – Kyle Oman Jul 25 '14 at 23:00
• Thank you for your suggestion @Kyle.I will make sure to be more specific from next time. – Freya Jul 27 '14 at 10:18

Thermal velocity is the velocity that a particle in a system would have if its kinetic energy were equal to the average energy of all the particles of the system.

Take an ideal gas in three dimensions as an example. In equilibrium there is a distribution of velocities among all of the particles. Some move "fast" others move "slowly". That means that there is a distribution of kinetic energy as well. You can calculate the average kinetic energy, call it $E_{avg}$ by adding up the energies of all of the particles and then divide that by the number of particles. It turns out that the average kinetic energy can be calculated for systems in equilibrium. For an ideal gas, $E_{avg} = \frac{3}{2} kT$. Average energy is proportional to the temperature of the system. There are similar expressions for more complicated systems, but the average energy is always proportional to $T$.

The thermal velocity is the speed that a particle would have if its kinetic energy happened to be equal to the average value. Thus for an ideal gas $$\frac{1}{2}mv^2 = \frac{3}{2}kT$$ and $$v = \sqrt{\frac{3kT}{m}}$$ For a system of particles of known mass, the thermal velocity depends only on the temperature and a universal constant. Thus, it is an indirect measure of temperature.

As you can see from the Wikipedia article, there are different ways to express average energy. This is one of them. The different ways lead to slightly different expressions.

• Thank you so very much @Garyp! The way you explained was so better and easy.Now I can visualise too. Thanks. – Freya Jul 27 '14 at 10:16

The statement you've provided means that thermal velocity is the velocity of particles present in a matter. Thermal energy is a form of energy which exists in the form of vibrations of particles in a matter. This means that thermal velocity depicts the velocity of particles in a system as well as heat or temperature in it.

Nifty, The thermal velocity is velocity of thermal motion of particles which make up gas, liquid, and so on. Thermal velocity is a measure of temperature and is also measure of the width of the peak in the Maxwell–Boltzmann particle velocity distribution.