In a gas that contains N molecules, is it accurate to say

Problem 26DQ

In a gas that contains N molecules, is it accurate to say that the number of molecules with speed v is equal to f(v)? Is it accurate to say that this number is given by Nf(v)? Explain your answers.

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In a gas, all the molecules move in a random motion, which means the direction and magnitude of the speed of each of the molecules is different. Since the molecules are in random motion, therefore they can collide with each other and the wall of containers but it cannot be explained by the distribution function of the speed. Thus, it is not accurate to say that the distribution function can explain the speed of a number of molecules.