How many molecules will hit the cylinder: Was my solution correct?

[Nirmal Padwal]

Homework Statement

Suppose that, in a partial vacuum chamber having 3 molecules of air per cm$^3$, a cylindrical object of radius 10cm and length 40cm is to be moved in a straight line from point A to point B with its axis along the direction of motion. The distance bet4ween A and B is 50cm. How many molecules will hit the cylinder in its entire journey?

Relevant Equations

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This is what I did, the cross-sectional area of the cylinder is $\pi 10^2 = 100\pi$ cm. Further, as the cylinder is moving a distance of 50cm. Thus, the total volume of vacuum, object covers throughout its journey is $100\pi \times 50 =5000\pi$ cm. Assuming that the molecules are uniformly distributed in the chamber, the number of molecules hitting the object is $5000\pi \times 3 = 15000\pi \approx 47124$ molecules.

Is this solution correct? I was confused because if it were, why was the length of the object given?

 

[collinsmark]

Homework Statement:: Suppose that, in a partial vacuum chamber having 3 molecules of air per cm$^3$, a cylindrical object of radius 10cm and length 40cm is to be moved in a straight line from point A to point B with its axis along the direction of motion. The distance bet4ween A and B is 50cm. How many molecules will hit the cylinder in its entire journey?
Relevant Equations:: .

This is what I did, the cross-sectional area of the cylinder is $\pi 10^2 = 100\pi$ cm. Further, as the cylinder is moving a distance of 50cm. Thus, the total volume of vacuum, object covers throughout its journey is $100\pi \times 50 =5000\pi$ cm. Assuming that the molecules are uniformly distributed in the chamber, the number of molecules hitting the object is $5000\pi \times 3 = 15000\pi \approx 47124$ molecules.

Is this solution correct? I was confused because if it were, why was the length of the object given?

It looks good to me.

But keep in mind your solution is only valid if the gas is very cold or if the rod moves through it very fast, or both. In other words, it ignores the gas molecules hitting the rod due to thermal reasons.

So why is the length of the rod given? It could be important if the thermal characteristics of the gas are to be considered, along with the speed of the rod. Maybe this will be given to you in a future exercise.

 

[Nirmal Padwal]

Thank you @collinsmark

 

[phinds]

Sometimes, extraneous but natural sounding information is given in a problem statement to make sure that a student can separate the wheat from the chaff.

 

[Vanadium 50]

Sometimes, extraneous but natural sounding information is given in a problem statement to make sure that a student can separate the wheat from the chaff.

I had a chemistry test once, multiple choice, where we had to identify the irrelevant statement in the problem.