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$\bullet$$\bullet$ A flask contains a mixture of neon (Ne), krypton (Kr), and radon $(\mathrm{Rn})$ gases. Compare (a) the average kinetic energies of the three types of atoms; (b) their root-mean-square speeds. (Hint: The periodic table in Appendix C shows the molar mass(in $\mathrm{g} / \mathrm{mol}$ ) of each element.)

a- The Average Kinetic Energy is the same for Ne, Kr and Rn$\mathbf{b}-\left[v_{r m s}\right]_{N e}>\left[v_{r m s s}\right]_{K r}>\left[v_{r m s}\right]_{R n}$

Physics 101 Mechanics

Chapter 15

Thermal Properties of Matter

Temperature and Heat

The First Law of Thermodynamics

The Second Law of Thermodynamics

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this's checked her 15 problem over 28 we have a flask that contains a mixture of neon, krypton and Radan gases. Um, we're asked to compare the average kinetic energy of these three types off off gases. So well, average kinetic energy for remember, kinetic energy average equals to help him 2/3 k times t write. So if this mixture is kept at a constant temperature for all these no, for all the the three gases and we have that their kinetic energy is going to be equal to each other, right? So they hole have the scene. Americ energy because it only depends on the temperature doesn't depend on the solar masses or anything. So they have the same Connecticut now far be were asked to compare the R. M s speeds for all three. In order to do that, let's remember the definition of the Army's speed. So it's gonna be three Katy over the Moler mess. So then this term, the Aramis speed is actually going to depend on what kind of guests we have. Boy, don't know. We have me on Krypton rain on because they will have different Mueller. NASA's right. So let's start. Where? For me. I free zone people. If we want to write the ROMs of neon, then we're going to use three. Katie divided by the Moler Mouths off your gas. Right. So then this from what it is, we can look it up from the periodic table. It's gonna be 20. Wouldn't want age grams for pull for me on. So for her, go on. How a mass speed for Krypton is going to be three Katy over molar mass of Krypton. Let's remember, the more massive Krypton is 83.8 friends for hope. And lastly, let me be here for a raid on we have our mess of greed are equals two, three, Katy over. Moller mess off radar. Right? And that is going to be all the more must celebrate on. If we look it up, he's going to be 222 grants for malls. Now again, we're not giving the temperature. We are not explicitly calculating the armistice feeds for each tough guess. But we are comparing them to each other. Remember of every compartment to each other, The easiest way to compare is going to be taking the ratio all the Aramis speed of let's say neon to prepped on neon to raid on and crypt on the raid on. So let's do that on the on the new page. So if we're fighting the ratio of the r m s speed or let's save me on over the armas speed off krypton, they're from the definition for each arm s speed for neon was three Katy over Mueller Mass of neon. Right? And now, in denominator, we have the arm a speed of her PDA. So it's going to be the law. Massa crypt off, right? We're inverting it because it's a denominators divided by three Katie. Now you can see how you can see that through three Katie's they're going to cancel each other out. Square roots R What's there to stay for me? So they're going to stay, But you can't, sir, wins, Right, So we have them. Is this ratio is is going to be a spirit from the moment mass of Krypton divided by Moller Mass off, you know? Then let's remember what these values were for Krypton. We have 83.8, and for yeah, we have 20.18 So squared insects. Where would we have 83.8 cramps from all in denominator, We have 20.1 Hate France promote. Then this ratio is going to turn out to be 2.4. Now you do the same for him, miss, uh, you know, to breed off, right? Me? Then we're pretty much half began. We can explicitly, Right? Scored a three Katy over a molar mass of neon invert. Take the nurse off the premises off radar and fiend. What? We're going to have the mauler mess off. Raid on, right, Divided by will amass off me. Non all I am to see you. Logic. Previously that we produce, we followed. So now the more massive raid on wass 222 grams for all divided by 20 queen What? Eight friends for Hall. So then what we have is the ratio between two shoes. 3.3 chip when we take the square root. Now, lastly, our message Compare the arm a speed of huh pricked onto the Aramis speed of raid on. Then we're looking at the molar Atia off raid on to the moderation of Mueller Massa Tom. Then it's going to be equal to 222 grams Permal, divided by 83.8 grams for all sort of take discourage of this ratio, We could find that to me 1.63 so

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