Circular Motion: Find Argon Inhaled by Julius Caesar

[gkglock]

Homework Statement

I need help with this problem, don't really know how to get started. In 1 hour, about how many argon atoms do you inhale that Julius Caesar also inhaled. Assume Julius lived 50 years and 1 liter of air holds about 6x10^20 atoms of argon. Also, assume the atmosphere is 200km thick. Also, it gives a hint to use the volume of a sphere: 4*pie*R^3/3.

Homework Equations

I assume this involves circular motion somehow. And we have a time, so maybe the equation a = 4(pie)^2*R/T^2 can be of use. Also, I need to involve the volume of a sphere somehow.

The Attempt at a Solution

Dont really know how to get started that's all I really want help with. Maybe a = 4(pie)^2*radius of the earth/50^2. To get started, don't really know what to do.

 

[lewando]

How much air did Julius process with each breath? What was his breath rate? What assumptions about the distribution of argon in the 200km atmosphere would you like to make?

 

[gkglock]

It says to assume that he had a normal breath rate, and nothing about how much air he inhaled with each breath. And I assume that the atmosphere is uniformly dense.

 

[lewando]

Step 1: Take the question of how may argon atoms did Julius inhale during his lifetime? Are we asking how many unique argon atoms he processed? Do we care about how many argon atoms he re-breathed? This is related to argon diffusion and is problematic for me because I don't know how to model that. How about for starters we assume instantaneous diffusion and the number of re-breathed argon atoms is negligible. What can you come up with?

 

[DaveC426913]

Make sure you state your assumptions. If you assume he does not rebreathe any atoms, say so.

What does circular motion have to do with this?

 

[gkglock]

Oh ok I think I get the idea or atleast the direction to approach this problem at. Reading this makes me wonder why i even thought circular motion. And no were not worried about the argon being re-breathed just how many you take in within an hour. So my guess is I would use the instantaneous velocity to reach how many I take in.

 

[lewando]

Not sure how instantaneous velocity would help. Think more about a function of breath rate, lung capacity, and argon in air.

 

[Kaxa2000]

Calculate volume of just the atmosphere of the earth

Measure how many breaths you take in 1 min and times it by 60 to get breath rate in one hour

Do the same for Julius in 50 years using your breathing rate = to his
Convert it to liters

I think 1 liter = 1 breath

Divide the total atmosphere volume by Julius total during lifetime

This should give you the amount of liters of air Julius has uniformly distributed I think

I feel kind of lost now but hopefully someone can expand on what I have or correct me if I'm wrong

But I believe the key here is through the assumption 1L of air holds about 6x10²⁰ atoms of argon. You have to find the amount in 6x10²⁰ atoms that belongs to Julius ceasar.

This is a real brain teaser for me