The graph at the right shows a Maxwell speed distribution for nitrogen molecules

Question

The graph at the right shows a Maxwell speed distribution for nitrogen molecules. Let vrms = the "rms" speed, vave = the average speed, vmp = the most probable speed. note: kB = 1.381 x10-23 J/K take: m = 4.65 x10-26 kg

e graph at the right shows a Maxwell speed distribution for nitrogen molecules. Let Vrms the "rms" speed, Vavethe average speed, Vmpthe most probable speed 0.I note: kB 1.381 x 10-23 J/K take: m = 4.65 x1026 k N molecules 7-29: K Answer the three questions below, using three significant digits 0.00 Part A: Which of the following are true regarding Vrms, Vave and Vmp? Vmp has the greatest value O Vave has the greatest value O Vrms has the greatest value O Actially, none of these are true 400 80 200 v (m/s) Part B: Which value corresponds to the peak in the speed distribution? Vrms O None of these mperature of the nitrogen gas was actually 4.50 x 102 K. What would be Part C: Suppose that the value of Vrms? Number Vrms m/ s

Explanation / Answer

A.) Vmp = (2kT/m)1/2

Vavg = (8kT/m)1/2

Vrms  = (3kT/m)1/2  

Clearly, Vrms has the greatest value

B.) The peak corresponds to Vmp . Maximum number of molecules have this speed. That is why it is called the most probable speed.

C.) Vrms = (3kT/m)1/2  = (3 x 1.381 x 10-23 x 4.5 x 102 / 4.65 x 10-26  )1/2  = 633.194 m/s

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