Problem

$\bullet$$\bullet$ Helium gas expands slowly to t…

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Problem 72 Hard Difficulty

$\bullet$$\bullet$ Atmosphere of Titan. Titan, the largest satellite of Saturn, has a thick nitrogen atmosphere. At its surface, the pressure is 1.5 Earth-atmospheres and the temperature is 94 $\mathrm{K}$ . (a) What is the surface temperature in $^{\circ} \mathrm{C} ?$ (b) Calculate the surface density in Titan's atmosphere in molecules per cubic meter. (c) Compare the density of Titan's surface atmosphere to the density of Earth's atmosphere at $22^{\circ} \mathrm{C} .$ Which body has a denser atmosphere?

Answer

(a) $-179^{\circ} C$
(b) $1.2 \times 10^{2}$ 6molecules/m
(c) $2.5 \times 10^{2} 5$ molecules/m $^{3}$

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Video Transcript

this is Chapter 15 Problem number 72. Um, we're given the fact that the settle, like Titan has a very thick nitrogen atmosphere. The pressure here on the surface of Titan of his 1.5 atmospheres and the temperature is 94 cabinet on the surface, so even part. They were asked what the temperature would be in Celsius in order to do the conversion is pretty straightforward. We only subtract 273 from 94. So then we figure out that it's minus its negative. 179 Celsius. This is unimaginably cold, right? So park be. We're asked to calculate the surface death density in Titan's atmosphere in molecules per meter cubed so surface, then city, Um, in that Titan's atmosphere in molecules for meter. Cute. OK, now, in order to do this, let's write down the ideal gas law PV equals and K t correct end being here, the number of molecules babying the volume So eventually what were essentially what we're asking, what we're looking for is N Overby, right? Molly goes per meter cube. So how to get there if we divide both sides by the Katie for instance, the K t here on the left, Inside the volumes. They're gonna cancel out. Katie. Katie, they're even canceled. And on the right hand side, we have an over V which would give us molecules in a cubic meter. Right? So then and over a B equals two p over K. T. Since we know the temperature and the pressure, we should be able to calculate and over be right. It's pretty straightforward except well, listen, Burt won five atmospheres, two passports, so it's gonna be one kind. You're a one time center for five fastballs for atmosphere, right. Divided by 1.381 time center were negative. 23 Jules, her molecule times. Calvin, this is our K. And then the temperature is given to us as 94 cabinet. Right. So from here and over, V will be one going to tense tantric or 26 molecules. Her cubic meter in part C were asked basically the same calculation density off. Um, while the surface density and molecules per meter cubed. Now this time off, er ds Earth's atmosphere so reverse at Atmos atmosphere, we know the pressure to be one atmosphere on the surface and the temperature to be 22 south Seuss. So again, handover V from the equation that read arrived previously in part B. C. This Endeavor V's gonna be able to pay or a P over Katie Orscher again. One atmosphere. Let's convert that Thio passed balls times 10 to 4 or five possible her atmosphere divided by 1.381 time center for negative 23 stools for for molecules Calvin and then the temperature is gonna be 22. However, we need to convert this to Calvin, so we're gonna have 273 to it. Here, the density would be 2.5 times 10 to worth 25 molecules tour cubic meter. All right now, in the second part of Part C were asked to compare this density two titans. So let's remember what titans density waas he It's 1.2 times 1.2 10 to 26 Ah, complete two times. Tentacle 26 is tightens much denser than the Earth's, Obviously right? So it's almost what one one kiss almost

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