Problem

$\bullet$ In a certain chemical process, a lab te…

02:04

Problem 42 Hard Difficulty

$\bullet$$\bullet$ Work done by the lungs. The graph in Figure 15.33 shows a $p V$ diagram of the air in a human lung when a person is inhaling and then exhaling a deep breath. Such graphs, obtained in clinical practice, are normally somewhat curved, but we have modeled one as a set of straight lines of the same general shape. (Important: The pressure shown is the gauge pressure, not the absolute pressure.) How many joules of net work does this person's lung do during one complete breath? (b) The process illustrated here is somewhat different from those we have been studying, because the pressure change is due to changes in the amount of gas in the lung, not to temperature changes. (Think of your own breathing. Your lungs do not expand because they've gotten hot.) If the temperature of the air in the lungs remains a reasonable $20^{\circ} \mathrm{C},$ what is the maximum number of moles in this person's lungs during a breath?

Answer

$\mathbf{a}-7.4 \mathrm{mm} \mathrm{Hg} \cdot \mathrm{L}$
$\mathrm{b}-0.059 \mathrm{ml}$

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Video Transcript

this is Chapter 15. Problem number 42 were given a PV diagram off inhaling and exhaling and breath were asked, How many jewels a network does this person's love do during love? Complete breath. So we were asked to calculate the network. As you remember, the area and closed by this of inhaling and inhaled curves are gonna give us the work done. So given that every box has the dimensions off, want me the meter off Mercury and then 0.1 leader If you can count the number of tiles enclosed here, it's around 75 There, 75 of them. So the area of each one. If we calculate that the area of what box area, let's say that is gonna be equal Thio one millimeter of, um, Mercury Times 0.1 leader. So for the work done, we have almost 70 pub of, um right, 75 times the area of the box that lets instead of using one millimeter mercury. Let's convert that the Paschal's so one millimetre off America is gonna be 133.3 passed balls right? And as you know, one leader is 10 to the power one leader is tempting for negative three meter cubed right? So, UM, let's convert that. It's a one millimeter of America real. It's 133.3 past bubbles here instead of 0.1. Let's do one time sent to make it three. Neater cute, Which means it's almost one Jules off work that person does. What completing the cycle now? In Part B, we are asked, asked Thio. Figure out number of bowls off air that we have in our lungs when TV is maximum. So when P Times be his neck, Sim, um, we're asked to calculate the number of most. First of all, when those did the gauge measure, where is the maximum point on the graph that is given to us? So if you could look at this point, our p e. The gauge measures the pressure here to be 11 millimeter off mercury and then the being at this point as 1.4 leaders, right? That's the maximum point where TV becomes maximum. But again, this is the gauges measurement, right? So let's say P Gage measures 11. Pardon me. He said that it was 11 right, 11 kilometer off America ary and the the maximum that point his 1.4 leaders. The real pressure, though, equals to the gauge pressure. The pressure that we measure with Gage the air pressure, right? So the air pressure would be. It's just one that most fear, right? So it's 760 tours and get now while we're for pressure and we have various units, as you know, So one centimeter also, let's put that down off Merrick. Yuri is also one. You're right. So let's write everything in terms of pores, that 11 millimeter roll off mark you is gonna be 11 4 and then the air has 760 pores, so it's 771. Tour of pressure. Now let's convert that seven under the 70 War tour to pass goals. It ordered Thio do that. We're gonna again multiply this by 133.3 of hospitals in the core so that we have WAAS with free time set for five hospitals as her pressure. Now, if you calculate the TV the maximum, then that is going to be equal to well point of three times Center for five. Paschal's times 1.4 leaders. Let's convert that to meters right from negative three. Peter Jukes, unit leader. So the MPV maximum is gonna be 100 and 44 meters. All right, now we know P V necks. However you calculate the number of bowls from there is from the ideal gas law. Right? The NOPD right hand side is an Artie. If you divide both sides by r t, then Petey, calculated to 144 meters divided by our is 8.315 jewels for mole kelvin. And then the temperature is 273 plus 20 Calvin, right? I did that conversion by adding 273 to our south seas value. Then from here we find the number of most to be 0.6 outs.

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