Kinetic Theory of Gases

The molecules of an ideal gas have a range of speeds. When an individual molecule collides with another one its speed and direction changes, but as long as the temperature is constant, the distribution of speeds remains the same.The root mean square speed c_rms of the molecules is the square root of the mean of the squares of the speeds of all the individual molecules. If the temperature is increased, c_rms increases and the distribution is flatter and broader.The kinetic theory equation for an ideal gas is: pV = ⅓Nmc_rms². The mean kinetic energy of a molecule ½mc_rms² = ³/₂kT where k = R/N_A.