1. (1) Use the Maxwell speed distribution function F(v) for an ideal-gas particle to derive the most probable speed v*, average speed u = (v), root-mean-square speed vyms = V(u2) = 3K5", where mis the mass of the ideal-gas particle, kg is the Boltzmann m constant, and T is the temperature. (1I) prove that Vrms >i >v*. (III) Rewrite the Maxwell speed distribution function F(v) as a function related to and v*, i.e., F (, v*). How much percentage do ideal-gas particles distribute at v*±(0.5% v*), v±(0.5% v*), and vms±(0.5% v*), respectively? (IV) Use the Maxwell velocity distribution function f (T) to determine the average velocity of the ideal gas (ī).

1. (1) Use the Maxwell speed distribution function F(v) for an ideal-gas particle to derive the most probable speed v, average speed u = (v), root-mean-square speed vyms = V(u2) = 3K5", where mis the mass of the ideal-gas particle, kg is the Boltzmann m constant, and T is the temperature. (1I) prove that Vrms >i >v. (III) Rewrite the Maxwell speed distribution function F(v) as a function related to and v, i.e., F (, v). How much percentage do ideal-gas particles distribute at v±(0.5% v), v±(0.5% v), and vms±(0.5% v), respectively? (IV) Use the Maxwell velocity distribution function f (T) to determine the average velocity of the ideal gas (ī).