Root mean square speed

Definition

Root mean square speed is the measure of the average speed of particles in a gas, calculated as the square root of the average of the squares of individual particle speeds. It is mathematically expressed as $v_\text{rms} = \sqrt{\frac{3kT}{m}}$, where $k$ is Boltzmann's constant, $T$ is temperature, and $m$ is the mass of a gas particle.

5 Must Know Facts For Your Next Test

1. Root mean square speed increases with temperature.
2. It depends on both temperature and the mass of gas particles.
3. The formula for root mean square speed is $v_\text{rms} = \sqrt{\frac{3kT}{m}}$.
4. At a given temperature, lighter gas molecules move faster than heavier ones.
5. Root mean square speed provides insight into the kinetic energy distribution in a gas.

Review Questions

• How does an increase in temperature affect root mean square speed?
• What variables are included in the formula for root mean square speed?
• Why do lighter gas molecules have higher root mean square speeds than heavier ones at the same temperature?

Related terms

Kinetic-Molecular Theory:

A theory that explains the behavior of gases in terms of particles in constant, random motion.

Boltzmann's Constant: $k$, a fundamental physical constant that relates energy at the particle level with temperature, equal to $1.38 \times 10^{-23}$ J/K.

Maxwell-Boltzmann Distribution:

A probability distribution used to describe the speeds of particles within an idealized gas.