- #1
PhysicsKush
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- Homework Statement
- At what pressure (at room temperature) would the mean free path of air molecules reach a macroscopic scale like ##10## cm ? Explain (qualitatively) what would happen if we tried to propagate a sound wave of wavelength ##1## cm in these conditions.
- Relevant Equations
- $$ l \approx \frac{1}{4 \pi r^{2}}\frac{kT}{p}, $$
I answered the first part of the question where I estimate the radius of ##O_{2}## is ##\approx 1.5 \times 10^{-10} \ \text{m}##:
$$ p = \frac{KT}{l 4 \pi r^{2}} = \frac{(20+273.15)(1.38\times 10^{-23})}{(0.1)(4\pi)(1.5 \times 10^{-10})^{2}} = 0.143 \ \text{Pa}.$$
The confusion arises on the second part of the question. Intuitively I'm thinking that a wave sent through a medium compresses and decompresses periodically the molecules it goes through. If the wavelength is ##1##cm and the mean free path is ##10##cm , then I believe the mean free path will increase by a factor of ##10##? I'm not sure what to think of this problem. Any insights would be appreciated.
$$ p = \frac{KT}{l 4 \pi r^{2}} = \frac{(20+273.15)(1.38\times 10^{-23})}{(0.1)(4\pi)(1.5 \times 10^{-10})^{2}} = 0.143 \ \text{Pa}.$$
The confusion arises on the second part of the question. Intuitively I'm thinking that a wave sent through a medium compresses and decompresses periodically the molecules it goes through. If the wavelength is ##1##cm and the mean free path is ##10##cm , then I believe the mean free path will increase by a factor of ##10##? I'm not sure what to think of this problem. Any insights would be appreciated.
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