For each breath that you take, how many of the air molecules would also been breathed by the patron saint of Physics, Sir Isaac Newton (1642-1727)during his life time, the atmosphere is about 8 km high, and the molecules in the air each occupy a space representing a little cubic box about 3.33*10^-9 m along a side, the earths radius is 6..38*10^6. make any reasonable assumptions for any data needed.

a) 6
b) 6*10^3
c) 6*10^6
d) 6*10^9
e) 6*10^12

Question

For each breath that you take, how many of the air molecules would also been breathed by the patron saint of Physics, Sir Isaac Newton (1642-1727)during his life time, the atmosphere is about 8 km high, and the molecules in the air each occupy a space representing a little cubic box about 3.33*10^-9 m along a side, the earths radius is 6..38*10^6. make any reasonable assumptions for any data needed.

a) 6 
b) 6*10^3 
c) 6*10^6 
d) 6*10^9 
e) 6*10^12

anonymous · Answer

Do you have any ideas on how to start?

anonymous · Answer

Assume 12 breaths per minute and a tidal volume of 1 liter. = 12 liters/minute = .2 liters/second Newton's age = 83 Assume avergage rate of intake between 0-20 = 1/2 of adult Number of molecules Newton breathed Volume inhaled lifetime = .2 l/s * (83-10)years V = 4.6x10^8 liters Volume of Earth's atmosphere = 4/3 π ((radius(earth+atm))^3 - (radius(earth))^3) V.e.atm = 4/3 π ((6.378x10^6m)^3 - (6.370x10^6m)^3) V.e.atm = 4 x10^18 m^3 = 4 x 10^21 liters Number of molecules per breath =.001m^3 (this is equal to 1 liter) / (3.33x10^-9)^3 = 2.7 x 10^22 molecules Number that Newton breathed: 2.7x10^22 * 4.6x10^8 liters/4x10^21 liters = 3.11 x10^9 molecules http://answers.yahoo.com/question/index?qid=20090402221619AA00x7n

anonymous · Answer

thanks dude!

anonymous · Answer

dang that's a lot of work^^

anonymous · Answer

Your welcome(: I didn't quite get it, so hopefully this answer from another user helps!

anonymous · Answer

|dw:1346786463146:dw| The first step is to find the number of molecules of air in one breath, for this you need the total volume of the air that a person breaths. For this we need the number of breaths and the volume of each breath. divide this total volume breathed by a person in a lifetime by the volume of one air molecule and you get the answer. 

Volume of one molecule is the volume of a cube of side 3.33*10^-9m. $$Volume-of-a-cube= (Side)^3$$When you have both you can find the number of molecules 'N_b' by$$ N_b= \frac{V_B}{Volume-of-one-molecule}$$
Also, if we were asked top find the number of molecules of air in the atmosphere, then it would be N_a where$$N_a=\frac{V_A}{Volume-of-one-molecule}$$