Root Mean Square Velocity

📊 intermediate

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

The average speed of gas particles as determined by their kinetic energy.

Variables & Units

$R$

Universal gas constant

Unit: $8.314 J/(mol \cdot K)$

$T$

Absolute temperature

Unit: Kelvin ($K$)

$M$

Molar mass

Unit: $kg/mol$

Key Information

📐 Derived From

Equating kinetic energy $\frac{1}{2}mv^2$ to $\frac{3}{2}kT$.

💡 Example

RMS speed of oxygen molecules at room temperature.

🔧 Applications

Gas diffusion and effusion calculations.

⚠️ Constraints

Applies to ideal gas behavior.

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