Suppose I have 2 identical boxes and both of them are divided into 2 equal halves by a board. Now I fill the 2 boxes with different total number of air particles, and with different number of air particles in the 2 halves of each box, so that in box A, the ratio of particles in the 2 halves of the box is 1:19, while in box B the ratio is 991:1009. Both boxes have a difference of 18 particles between the 2 halves, however the concentration gradient in box A is much larger. Is the pressure produced in box A larger than in box B, or do they have the same pressure? (Assuming uniform temperature and other variables can be neglected)
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asked Sep 28, 2019 at 10:16
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$\begingroup$ What does the ideal gas law predict? $\endgroup$– Chet MillerSep 28, 2019 at 12:14
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$\begingroup$ Same pressure? Since it only depends on number of moles $\endgroup$– never took courses but whySep 28, 2019 at 12:28
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1 Answer
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As Ched Miller points out ideal gas law (https://en.m.wikipedia.org/wiki/Ideal_gas_law) states that PV=nRT, with P = pressure, V = volume, n = number of moles, R = constant, T = temperature. Since V, R and T are the same in all your half boxes, you are left with P = k n, k being a constant. In other words, pressure will be linearly proportional with the number of particles. Then the pressure difference in box A will be proportional to 19-1, while the other to 1009-991, 18 in both cases, so same pressure applied on the two boards.
