72 pr 96 dpi web design?
Out of context: Reply #34
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- pmarckesano0
There you go again Ribit, confusing the kids...
Interesting question, however...
If you have a bunch of gas in a box, and then you fly past that box at near-lightspeed, you are correct that the length of the box will appear to change, shrinking the volume (V) of the box by some factor 1/gamma.
The same number of particles are now in a smaller box, so the density goes up by the same factor gamma. But there's also an apparent slowing down of the gas relative to the walls, by a factor gamma-2, so the number of particles hitting the walls (per unit of observed time) actually goes DOWN by a factor of 1/gamma. However, each collision supplies more momentum to the walls (by a factor of gamma -- although this calculation is far from trivial) so all these effects exactly cancel: the pressure (P) stays the same. (All this analysis is just for the walls that are at the "front" and "back" of the moving box; the walls to the side have a different analysis I won't get into, but it gives the same answer...)
Now, if PV=NRT still holds, the above analysis tells us that T must drop by a factor of 1/gamma, to balance the drop in V. Would that mean that water vapor at 101o C could appear to be only 99o C in a different frame and condense to water? Einstein tells us this CAN'T happen -- the same phenomena must have consistent explanations in all reference frames, and the difference between steam and water is too great. But does that mean that water has a different condensing temperature in different frames? Or does PV=NRT not work in some reference frames? There appears to be a paradox here: it looks like SOME physics has to be different... This, I presume, is the heart of your question.