1. (a). Generate Köhler curves for particles of both...

1. (a). Generate Köhler curves for particles of both (NH$_4$)$_2$SO$_4$ ($ ho$ = 1.8 g cm$^{-3}$) and NaCl ($ ho$ = 2.2 g cm$^{-3}$) with radii of 0.01, 0.1, and 1.0µm. Overlay a pure water curve for comparison. (b). Discuss the differences and similarities in these curves. Where are they similar, and why? Where are they different, and why?

Transcript

00:01 We have two particles here.

00:03 We have taking paths t, sine t, cos t, and t, 0, 1.

00:12 We'd like to describe any intersections of the curves.

00:15 Well, that would mean that t equals t, for the x component.

00:20 Sine t equals 0, and cos t equals 1.

00:24 That is to say they're the same x -coordinate, the same y -coordinate, the same z -coordinate.

00:28 T equals t is vacuous.

00:29 It's always going to be true, so you don't need to worry about that.

00:33 Sine t equals 0 tells us that t is a multiple of pi.

00:37 And cos t equals 1 tells us that t is a multiple of 2 pi, which means that these are going to intersect whenever t is an integer multiple of 2 pi, which is great.

01:05 Well, ok, that's precise.

01:06 These are the values of t.

01:07 We're going to do that.

01:08 So this way, i've actually skipped ahead.

01:09 This is part b.

01:11 The intersections of these curves are just going to be, let's see.

01:18 So t, sine t, cosine t is going to be a helix in the x direction, x helix, going around the x -axis.

01:34 So if we have this is the x -axis, our y and our z are going to spiral around the x -axis, something like this.

01:46 Whereas this is just a path with z equals 1, y equals 0.

01:53 So it kind of goes along like that, which, of course, because they have the same x value at all points t, are just going to intersect whenever the lines intersect, which is great...

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