College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
The root-mean-square (rms) 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 an important parameter in understanding kinetic theory and temperature relations.
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RMS speed is given by the formula $v_{\text{rms}} = \sqrt{\frac{3kT}{m}}$, where $k$ is Boltzmann's constant, $T$ is the absolute temperature, and $m$ is the mass of a gas particle.
RMS speed increases with temperature; as temperature rises, particles move faster on average.
At a given temperature, lighter gas molecules have higher rms speeds compared to heavier molecules.
RMS speed provides insight into the kinetic energy distribution among gas particles and helps explain pressure and temperature relationships in gases.
It plays a crucial role in deriving other thermodynamic properties like diffusion rates and mean free path.
Review Questions
What is the formula for calculating RMS speed?
How does RMS speed change with increasing temperature?
Why do lighter gas molecules have higher RMS speeds at the same temperature?
Related terms
Boltzmann's Constant: $k$ is a fundamental physical constant that relates the average kinetic energy of particles in a gas to the temperature. Its value is approximately $1.38 \times 10^{-23}$ J/K.
Kinetic Energy: $E_k = \frac{1}{2}mv^2$, representing the energy an object possesses due to its motion. For gases, it relates to particle velocities.
Maxwell-Boltzmann Distribution: A probability distribution that describes the range of speeds among particles in a gas at thermal equilibrium.