Root Mean Square Speed

📊 intermediate

$$v_{rms} = \sqrt{\frac{3RT}{M}}$$

The measure of the speed of particles in a gas.

Variables & Units

$M$

Molar mass

Unit: $kg/mol$

Key Information

📐 Derived From

Equating kinetic energy to $3/2 kT$.

💡 Example

Calculating speed of Hydrogen molecules at room temperature.

🔧 Applications

Molecular diffusion and isotope separation.

⚠️ Constraints

Ideal gas.

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