A box with volume V confines 34 particles with identical mass m and the followin

Question

A box with volume V confines 34 particles with identical mass m and the following speeds: three particles with speed v, eight particles with speed 2v, five particles with speed 3v, three particles with speed 4v, thirteen particles with speed 5v, and two particles with speed 6v. (Use the following as necessary: v.)

(a) What is the most probable speed of the particles in this box?
vmp =  

(b) What is the average speed of the particles in this box?
vav =  

(c) What is the rms speed of the particles in this box?
vrms =  

Explanation / Answer

part a:

most probable speed is the speed with which most of the particles travel.

here as 13 particles (highest in the group ) travel with speed 5*v, most probable speed is 5*v m/s

part b:

average speed=total speed/number of particles

=(3*v+8*2*v+5*3*v+3*4*v+13*5*v+2*6*v)/34

=3.6176*v m/s

part c:

rms value =sqrt(sum of squares of all the velocity values/total number of particles)

=sqrt(3*(v)^2+8*(2*v)^2+5*(3*v)^2+3*(4*v)^2+13*(5*v)^2+2*(6*v)^2)/34)

=3.9295*v m/s

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