Question

The root mean square velocity (\(v_{\text{rms}}\)) of a gas is given by:

Hint:

The rms velocity provides an average measure of the speed of gas molecules, and it increases with temperature and decreases with molecular mass.

Answer 1

The root mean square (rms) velocity of a gas is calculated using the formula: \[v_{\text{rms}} = \sqrt{\frac{3kT}{m}}\] In this equation: - \( k \) represents the Boltzmann constant. - \( T \) denotes the temperature, measured in Kelvin. - \( m \) is the mass of a single gas molecule. This equation represents the square root of the average of the squared velocities of the gas molecules. Its derivation stems from the kinetic theory of gases.