The Kinetic Theory Of Gases

The quantities and are integrals involving the speed distribution function , and they represent different moments of the speed distribution. From the Maxwell-Boltzmann distribution, we know that the speed probability distribution is proportional to , where is the mass of the molecules and is the temperature. ### Step 1: Evaluate the relationship between and . - is the moment that involves the term, which has a higher dependence on the velocity and is affected more by higher speeds. - involves the term and is less dependent on higher velocities. In general, for any given distribution, the moment involving (which represents higher-order moments) will be smaller than the moment involving since the integrand in decays faster than that in due to the higher powers of . This means that: Thus, the correct relationship is .