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6L-elk 1(2205) (continjcdi Aauunanou: Lhill Ihc IaaL aie hul lull,0 Lhcrc SUlikr of liquid in Lc Enk at Sunaee Ihlt #ell-Inlxcu ualct 49 Iluxanz (Ut M thc tanz a[1 CC ~cp" minuta Mneml thc cunc 4 bclote;wilh < WariahlcKevbse your dillerential cquauca fromnclds thts Infurrnittion(6)52Atsole your colion Uine Euctk inlcgtling (1t0xts. Thcn fica ccIL wululion nen S(o) sprroximnalcly how much sk is In Ua tank #txn /% Iul !t ?5 T{ s( 2) tank fut whtv Tk Suppoxc that the tink bad infinitc volui

6L- elk 1 (2205) (continjcdi Aauunanou: Lhill Ihc IaaL aie hul lull,0 Lhcrc SUlikr of liquid in Lc Enk at Sunaee Ihlt #ell-Inlxcu ualct 49 Iluxanz (Ut M thc tanz a[1 CC ~cp" minuta Mneml thc cunc 4 bclote;wilh < Wariahlc Kevbse your dillerential cquauca from nclds thts Infurrnittion (6) 52 At sole your colion Uine Euctk inlcgtling (1t0xts. Thcn fica ccIL wululion nen S(o) sprroximnalcly how much sk is In Ua tank #txn /% Iul ! t ?5 T{ s( 2) tank fut whtv Tk Suppoxc that the tink bad infinitc voluie K cnuldk this Froces : indxlinilely woul thc long termn cutccntration ofslt he in the lank? Fird a such Uat thls concentrarion j 4 kg perlixtt: Lm S(t) 44 | 2 5 75 4 ( +44 ) Y75 ( (/2 +44 4hs Ykt 4 1 F44)



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(III) The quantity of liquid (such as cryogenic liquid
nitrogen) available in its storage tank is often monitored by
a capacitive level sensor. This sensor is a vertically aligned
cylindrical capacitor with outer and inner conductor radii $R_{\mathrm{a}}$
and $R_{\mathrm{b}},$ whose length $\ell$ spans the height of the tank. When a
and $R_{b},$ whose length $\ell$ spans the height of the tank. When a
nonconducting liquid fills the tank to a height $h(5 \ell)$ from
the tank's bottom, the dielectric in the lower and upper
region between the cylindrical conductors is the liquid $\left(K_{\text { liq }}\right)$
and its vapor $\left(K_{\mathrm{v}}\right),$ respectively (Fig, $33 ) .$ (a) Determine a
formula for the fraction $F$ of the tank filled by liquid in
terms of the level-sensor capacitance $C .[$ Hint: Consider
the sensor as a combination of two capacitors. $.$ (b) By
connecting a capacitance-measuring instrument to the level
sensor, $F$ can be monitored. Assume the sensor dimensions
are $\ell=2.0 \mathrm{m}, \quad R_{\mathrm{n}}=5.0 \mathrm{mm}, \quad$ and $\quad R_{\mathrm{b}}=4.5 \mathrm{mm} .$ For
liquid nitrogen $\left(K_{\mathrm{liq}}=1.4, \quad K_{\mathrm{V}}=1.0\right),$ what values of $C$
(in pF) will correspond to the tank being completely full
and completely empty?

This problem has you analyzing a scatter plot which are trying to recreate here. And the graph y equals X is on it. But this is not a least square regression line. So first, what is the overall pattern that we're seeing? So as we go from right toe laughed, the blue dots are all climbing upwards. That so the overall pattern seems to be that everything is going up as we go to the right now is the y equals X allying a good indicator for where a point should be. Well, we will get her line going a little too high, especially near the end. This line might not be the best line, so that should be a bit lower. We want it going through the middle of all of these clusters. So for this one, No. So what is the last part we're going to compare? Why equals X to the least square regression line? If we were to make the least square regression line, we would probably have it going look something like this, something like that, so we can get it going through as many of the points as possible. So what's different about the slow, but well, you noticed the Green Line. It's closer to being like this. It's closer to being completely horizontal, so the slope appears to be smaller and the Y intercept. We also want to compare that the why intercept If you notice is higher because it's intercepting the access, that's a higher point. So you have a smaller slope and a higher interceptor, all right, and we're doing.

All right, I need to recreate this table. one way, one cauldron, one bag, one possible and one girl. And then across across the top we got way cauldron bag possible. And gil 1 to 1 and ninth 43rd 640 and 120,000 200 40. Okay, so I just have to fill in these numbers. Much harder to draw horizontal lines and vertical lines, at least for me. Okay, uh 121121121121 It's always going to be 121 down the middle here. Now I here to here, it's just going to be the reciprocal. Okay, now what are we going to do here? A bag is how many cauldrons? Well, one bag is 3 40th of away, but a cauldron Is 3/10 of a way. Oh man, this may take some time. I here's I guess what I'm going to do, one bag and there are 4:30, bags in a way. And then we need to go from ways two cauldrons. Right, So 10 9th of a cauldron is a way, Wait a minute. What am I trying to do here? Going from bags to cauldron? All right, let me back up. I needed to reverse that. I need to put cauldrons in the denominator, 4/30 of a bag, 40 3rd of a bag that goes down here, so I can cancel out the bags. That's going to be one way. Now I need to write ways down here And that's going to be 10 9th of a calder. Okay, so that's going to be 3/40 6 times 10. 9th. Okay. Four mhm Three 1 12. So one bag is one, 12 And so now I can put 12 here. Now I'm going to start with one possible, we're going to put possible down here. Um and we know that 640 pod als is one way. Now we need to go from ways two cauldrons, um 9/10 of a cauldron is a way, so ways cancel out paddles cancel out. And it's not nine tens, it's 19th of a cauldron is away. Okay. 1/9 times 64. 576. Okay, that's gonna be one over 576 And this is going to be 576. Okay, let's try to find some more room, but I'm not sure I can find more room on here. Into black one pot to a bag. Well, we got to go to way first And then we need to go to a bag. 43rd of a bag is away. Way, way possible possible. Okay, so that's gonna be 40 Over three times 640. Okay. 640 divided by 40 is 16. 16 times three is 48. Okay, now we've got to get these, so we're going to start with a gill, We move down a little bit one gil, I didn't know there were two Ls and gills. Okay. One gil and away Is 1- 0- 40 Gil. Now way, two Children 10 nights where Children is away, so that would be um And the denominator, we're going to have clear nine times 1 to 0 24 108216. Okay. Now what I'm just gonna do is I'm gonna erase here. And all I gotta do is bags in a way. 43rd bag in a way. Okay, so 1 to 0-40, divided by 40 3006, 3006 Times three, 9018. One more one way is 640 possible. Okay so now I need to do 1 to 0 240 divided by 640 Uh Doesn't give me a nice number. Wait a minute, I'm just going to put it in and simplify the fraction 640 over 1: 0- 40. Hey now simplify domain Air. Okay. My calculator doesn't want to simplify that. Okay well it's 64 Over 120 24 Um 1-0 2 4 divided by eight Is 1503. Okay. And there you have it. We can now make conversions for witches brew. Mhm. Yeah.

Let he does ed is there a specific volume? Of course for me there's new special volume of pepper. Yeah that we will be the original bottom of pepper. Yeah then we can write and tv upon arctic to equal to mass of liquid into mass of pepper. That is we upon and readers were or be upon and it's good to mass of liquid any times more so pepper and to readers and so yeah and my husband into eman and two videos L. B B. B into one minus one upon and or be upon end and minus one. So efficiency will be and then we does upon The upon end that is N -1 upon Capital and -1 in kids. Okay. Mhm. When the final volume Yeah yeah of the suspect of the substance corresponds to the midpoint oh midpoint of our original portion of a gentle person. Of the ice. Of thermal line. I saw thermal line in PV diagram the finding volume must be uh huh one plus and into leaders and why to per unit mass of the substance. Oh this volume of the liquid is mhm. Is B that's held by two. But you need total mass of a substance but you need to delmas of the substance hence It is called to one upon. But listen that so thanks for watching it

I know that a T X Y diagram will show us the relationship between the temperature and the mole. Fraction of liquid and vapor stick teams at constant pressures. And we know that the lower carb and the graph is boiling carbon. The upper covers the Jew point carve. So what we have is a flow chart for the vaporizer. So we know that is equal to envy of an L on. Then with some substitution zones, we get a is equal to N B over an l is equal to x f minus X over. Why minus x f. So we know that except is not point for from the given T X y diagram, except is not point for X is not point to three and y is not 30.62 So we substitute these values in. We got no 0.4 take away, not point to three. Tried that by not 30.6 to take away, not point. Before we get a value of North 0.7727 that is, the fraction of feed vaporized what equals miles of paper divided by miles of liquid. So in the next part, the maximum minimum temperature at which are feed would be able to be separated into vapor and liquid. Uh, would be found when the feed mole Fraction cuts the boiling point. Carvin the Dew point curve So we have a team in is 75 degrees C. On the fraction of FIFA priced at this point is zero. Then we have t marks. We have 87.5 degrees on the fraction. That would be very surprised at this point would be one So team in 75 t max 85 on the final part here. So if the point C is condensed under the condensed into the constant pressure, so then we observed from the graphic composition of the liquids dream, it's not point to three and composition of the vapors not win 77 So the temperature of the stream leaving the condense size 80 degrees Celsius. So for the final party is 80 degrees Celsius. The composition of the liquid stream is not point to three on. Now we could like a paper that is not 27 7. Okay,


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