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 given by the formula: \[ v_{\text{rms}} = \sqrt{\frac{3kT}{m}} \] where: - \( k \) is the Boltzmann constant, - \( T \) is the temperature in Kelvin, - \( m \) is the mass of one molecule of the gas. This formula gives the square root of the average of the squared velocities of gas molecules. It is derived from the kinetic theory of gases.