physics

Thermal velocity

Thermal velocity is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Thermal velocity rather than just read about it. In short: Thermal velocity or thermal speed is a typical velocity of the thermal motion of particles that make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature.

Key takeaways

Thermal velocity belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Thermal velocity to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Thermal velocity from memory before moving on to harder problems.

Reference excerpt

Thermal velocity or thermal speed is a typical velocity of the thermal motion of particles that make up a gas, liquid, etc. Thus, indirectly, thermal velocity is a measure of temperature. Technically speaking, it is a measure of the width of the peak in the Maxwell–Boltzmann particle velocity distribution. Note that in the strictest sense thermal velocity is not a velocity, since velocity usually describes a vector rather than simply a scalar speed.

Definitions Since the thermal velocity is only a "typical" velocity, a number of different definitions can be and are used. Taking k B {\displaystyle k_{\text{B}}} to be the Boltzmann constant, T {\displaystyle T} the absolute temperature, and m {\displaystyle m} the mass of a particle, we can write the different thermal velocities:

In one dimension If v th {\displaystyle v_{\text{th}}} is defined as the root mean square of the velocity in any one dimension (i.e. any single direction), then

v th = k B T m . {\displaystyle v_{\text{th}}={\sqrt {\frac {k_{\text{B}}T}{m}}}.}

If v th {\displaystyle v_{\text{th}}} is defined as the mean of the magnitude of the velocity in any one dimension (i.e. any single direction), then

v th = 2 k B T π m . {\displaystyle v_{\text{th}}={\sqrt {\frac {2k_{\text{B}}T}{\pi m}}}.}

In three dimensions If v th {\displaystyle v_{\text{th}}} is defined as the most probable speed, then

v th = 2 k B T m . {\displaystyle v_{\text{th}}={\sqrt {\frac {2k_{\text{B}}T}{m}}}.}

If v th {\displaystyle v_{\text{th}}} is defined as the root mean square of the total velocity, then

v th = 3 k B T m . {\displaystyle v_{\text{th}}={\sqrt {\frac {3k_{\text{B}}T}{m}}}.}

If v th {\displaystyle v_{\text{th}}} is defined as the mean of the magnitude of the velocity of the atoms or molecules, then

v th = 8 k B T π m . {\displaystyle v_{\text{th}}={\sqrt {\frac {8k_{\text{B}}T}{\pi m}}}.}

All of these definitions are in the range

v th = ( 1.6 ± 0.2 ) k B T m . {\displaystyle v_{\text{th}}=(1.6\pm 0.2){\sqrt {\frac {k_{\text{B}}T}{m}}}.}

Thermal velocity at room temperature At 20 °C (293.15 kelvins), the mean thermal velocity of common gasses in three dimensions is:

References

Worked examples

Example 1 — a first encounter with Thermal velocity

Start with the simplest possible case. Write down what Thermal velocity claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Thermal velocity before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Thermal velocity ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Thermal velocity

In research: Thermal velocity appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Thermal velocity in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Thermal velocity is common in secondary-school and first-year university syllabi. It links to neighbouring topics Statistical mechanics, Statistical mechanics stubs, Thermodynamic properties, so understanding it makes those chapters shorter.
In everyday life: Look for Thermal velocity outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Thermal velocity in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Thermal velocity means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Thermal velocity out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Thermal velocity in simple terms?

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

Why does Thermal velocity matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Thermal velocity?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Thermal velocity.