SIN练习题第3题
3.For each breath that you take, how many of the air molecules would also have been breathed by the patron saint of Physics, Sir Isaac Newton during his lifetime (1642-1727)?
The atmosphere is about 8 km high, and the molecules in the air each occupy a space representing a little cubic box about 33.3 x 10 -9 m along a side. The earth's radius is 6.37 x 106 m.
Make reasonable assumptions for any data that you need!
(A) 6 (B) 6 X 10³ (C) 6 X 106 (D) 6 X 109 (E) 6 X 1012
SIN练习题3答案及解析
（答案：D）解析：If each breath of Sir Isaac's (and ours) is about 1 litre = 10-3 m3, and they are 3 seconds apart, then in 1727-1642=85 years, he will have had 85 x 365 x 24 x 3600 /3 = 8.93 x 108 breaths, for a total volume of 8.93 x 105 m3. We will assume that the air mixes well enough that we do not have to worry about air being breathed twice.
The total volume of the atmosphere is 4 RE 2 h, where RE is the Earth's radius, and h is the height of the atmosphere, giving 4.08 x 1018 m3. The fraction of air molecules ever breathed by the patron saint of Physics is thus 8.93 x 105 / 4.08 x 1018 = 2.19 x 10-13.
The number of molecules in each breath of ours is the density 1/(3.3 x 10-9)3 = 2.78 x 1025 m-3, multiplied by the volume of each breath, 10-3 m3, or 2.78 x 1022 molecules. Multiplying by the fraction breathed by Newton, each breath of ours has about 6.08 x 109 molecules also breathed by him (D). Since we have about 9 x 108 breaths, each breath of ours has about 7 molecules also breathed by Isaac Newton.
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