As the average molecular velocity is approximately equal to

Question

The number of molecules crossing a unit area per unit time in one direction is given by

where n is the number of molecules per unit volume and v is the average molecular velocity.

As the average molecular velocity is approximately equal to the speed of sound in a perfect gas, estimate the number of molecules crossing a circular hole 10^-3 in. in diameter.

Assume that the gas is at standard conditions. At standard conditions, there are 4 × 10²⁰ molecules per in.³.