The most probable speed of a gas molecule is given by V m p = 2 k T m

Question

A gas is cooled and trapped in a two-dimensional region by laser beams and magnets. The speed distribution function of the gas molecules obeys the two-dimensional Maxwell-Boltzmann distribution law, f(v)=2π(m2πkB T)ve−mv22kB T where m is the mass of a gas molecule, T is the temperature, and v is the speed. What is the average speed of the gas molecule?

Answer 1

Question

Chapter 21, Problem 21.42P

To determine

To show: The most probable speed of a gas molecule is given by Vmp=2kTm

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A gas is cooled and trapped in a two-dimensional region by laser beams and magnets. The speed distribution function of the gas molecules obeys the two-dimensional Maxwell-Boltzmann distribution law, f(v)=2π(m2πkB T)ve−mv22kB T where m is the mass of a gas molecule, T is the temperature, and v is the speed. What is the average speed of the gas molecule?

Only answer letters (d) and (e) a) Using the Maxwell-Boltzmann function, calculate the fraction of argon gas molecules with a speed of 305 m/s at 500 K. (ans: 0.0014) b) If the system in (a) has 0.46 moles of argon gas, how many molecules have the speed of 305 m/s? (ans: 6.44 x 10-4) c) Calculate the values of vmp, vavg, and vrms for xenon gas at 298 K. (ans: Vmp=194.2 m/s , Vavg=219.2 m/s , Vrms=237.8 m/s) d) From the values calculated in (c), label the Boltzmann distribution plot with the approximate locations of vmp, v avg, and vrms e) What will have a larger speed distribution, helium at 500 K or argon at 300 K? Helium at 300 K or argon at 500 K? Argon at 400 K or argon at 1000 K?

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