two-containers-are-at-the-same-temperature-the-gas-in-the-first-container-is-at-pressure-p_1-and-has

Question

Two containers are at the same temperature. The gas in the first container is at pressure $p_{1}$ and has molecules with mass $m_{1}$
and root-mean-square speed $v_{	ext { rmst }}$ . The gas in the second is at pressure 2$p_{1}$ and has molecules with mass $m_{2}$ and average speed $v_{\mathrm{avg} 2}=2 v_{\mathrm{msl}} \cdot$ Find the ratio $m_{1} / m_{2}$ of the masses of their molecules.

Sri Datta Vikas Buchemmavari · Accepted Answer

Now we&#x27;re given the pressures molecular masses on the Artemus and the average off particles two sets of gases You know that we oughta mus is squared off three rd by m So we are to miss one. It&#x27;s quid off three our teeth by m one. Similarly, we average too. We know the formula is squared off Aid Artie by pie. Um, so that&#x27;s a tarty Bye. Hi M to Now we know that the average two is twice we are miss one. So that&#x27;s two times It&#x27;s weird off three. Artie by m one. We also know that Muller mask is molecular mass times I&#x27;ve got your number. So em one by m too is someone by MT So from this equation, by swearing on both sides on canceling Artie, they see that 64 by hi M toe is equal new four times three by m one, now 64 4 times 16 in 64. Which means And when I am too, is which is also equal toe small in one very small himto is equal. Do three by by 16. And that is a uh what? I&#x27;m sorry. This is square just eight. Artie. So This is not 64. This is just eight I. So when you cancel it before, it turns out to be just too, which means this is simply three bye bye, too. On three. Pervy, too, is simply 4.71 so the ratio&#x27;s off. Molecular masses is 4.71 simple as that.

Michael Mackenzie · Answer

So we&#x27;re given that temperatures are equal between the two containers in that pressure, and one is half the pressure. P two, we&#x27;re not given m one or M two, but we aren&#x27;t given that the average velocity in the 2nd 1 is equal to twice the room means squared in the 1st 1 So to find em one over M, too, we start by writing the out these velocities in taking their ratio. So be too average over tea are a mess. The 1st 1 is equal to two in this equals, So the two average is square root. Hey, times, Artie, over. Pi empty. That&#x27;s our mess. Velocity just three. Artie over someone. So here are tease. Cancel. We just get the square root mm to Sorry one over. Pi times three. Mm. Two. So this here, we can just cancel out to just be Where were you? And little and one over three pie and two. So squaring both signs and moving this gate over three pie to the other side. We get four time three pie over eight equals and one over M too equals three pile or two, which is about 4.7

Hugh Ross · Answer

All right. So we have a problem where Container, eh? Has twice the volume of container. Be so I&#x27;m gonna make a big container, eh? Yes. We can visualize what&#x27;s going on. And then container be with approximately half the volume. All right? And container A also has half the number of molecules I&#x27;m gonna represent. Maybe four molecules in here that are in motion and B is gonna have twice the number. So have maybe eight molecules in there. So you can already see in a that it&#x27;s doesn&#x27;t It&#x27;s really big, and the molecules have lots of room to move. We know that pressure is directly proportional to the number of molecules. So we and and so this has a has half the number of molecules, so a is gonna have half the pressure. Okay, We also know that pressure is inversely proportional to volume, and A has twice the volume compared to be so it&#x27;s gonna have half the pressure 1/2 combined twice. This means that a is gonna have 1/4 off the pressure compared to be so, the ratio of the pressure of a compared to the pressure of B you pay is gonna have 1/4 of the amount of pressure in comparison. Now, if you&#x27;re an equation person, you might wantto jumper right to p equals. And Artie, um, over volume. So that&#x27;s the pressure. So let&#x27;s look at the ratio of the pressure of A to the pressure to be and, um, weaken. Write it like this. So a pressure has half the number of molecules, so I&#x27;m just gonna put in over two time. Some constant are times the temperature. Now the temperature is the same for both. Um, so I&#x27;m just gonna put t divided by the volume of a which is to times the compared to the volume of be OK now let&#x27;s look at the pressure and B B has a certain number of molecules. You have a constant same temperature. Bye. The original volume. OK, so a has some twice the volume. He just has the original volume. A has half the number of particles and be had the original number of particles. Look at what cancels here. You&#x27;re the same temperature, same everything cancels except the divided by two which comes in here twice. So we have 1/2 over too. So the ratio of P H A P B is a is 1/4 of the pressure off B. So that&#x27;s the ratio

Shital Rijal · Answer

Yeah, So we have here to add Antico containers, which have which has two types of gases A and B And he says the muscle someone you love gas off site E and me is three point before entered into the far my strangest seven Kinsey penned. It also says that myself, uh, when you&#x27;re up gas off divey his M B is equal to 5.34 Entertained the power. I must thank you six. So what gets us out under the same for sure that is preserved it. He is equal to the percentage on same Kim present that is t a musical to TV. And the temperature is Did you sense? Yes, convert this into Tell me that is a country of 83. So, Norma Question asks us for e which one could say rehab graded crosses can dignity, part molecule and Adam. Mrs Spitzer crosses her character&#x27;s hee hee three by two. Off was Vince Constant key and absolute temperature teeth. So in this case, in this case, temperature off he is a cold temperature. Therapy on Goldman&#x27;s constant B is constant for both gases, right? So this in place cross isn&#x27;t an indignity automatically a group That&#x27;s for the No. The second part off. He asks us a load of Adam. It is no Be Ademas Is your room trendier Treated, Katie. Bye, Massa Political despondent, right? So as we can see, the temperature is the same. So only difference up one is the mass now suits M e is list than Emma Fee. You can say that Be Adamis for be is less than be Adamis for a right. So which has the question is asking which had the greater Kandic energies, that is Our answer is great kind of dick energy. So greeter at a Mississippi. Uh, so next question, Peces. Now we want to raise the temperature off only one of the containers so that both have the same Adam assist, right? I would have to say about a Mr Disputed, which means that tender three key that&#x27;s it up one myself should be quite cool. Three kids. Good. So be it. One us off me, right? No, If we want this since m a. His list of m v for this condition. Easy quiet issued me less than you. Right, So we can say that. But it&#x27;s set up B shoot decrease. So are uncertainties. Okay? No, the next question. What temperature will you accomplish? Your goal. So, for what temperature will accomplish, we have adjusted to remind the band off TV. So from this from this equation here, the hell off TV can be calculated has do you easy, Quick Group md by me. You do do you soon. And bees 5.3 pools. You tipped into the power minus 26 one and is 3.3. Pull in return the bottom minus 27 on dhe. Temperance it off. He that is a conflict 183. So this gives me Do you be sure you do? Who fired good for if you wanted to. Since census, this comes out to eat. Who do? 51 seances. Right? So this gives me the temperature out TV when the boat and we will have the same out of Mrs Bute. So just to proximity now, as we have accomplished our rules that we have mere Aramis is your seem for book which would have a greater than indignity crosses. Who can you report money, Mel again. You have to compare easy call Truth three by Kitty Now if this time TV is greater than tea because we realized that give the same Adam&#x27;s dispute? Yeah, Cross isn&#x27;t indignity of B. We need to defend process, have dignity of a So were our answer keys. So in this way, we have completed the sunshine from this question. Thank you for watching.

Charles Thomas · Answer

So to calculate the, uh, root mean square speed, we first square each value. And so now I have written the squares in, and, uh, now we take the mean of the squares. We add up all the squares and then we&#x27;re going to divide by the total number of values, which is six. And once I do that, then I take the square root and I get to 0.77 in that. And that&#x27;s all. The values were in leaders per second, so I&#x27;d square. I mean, get major squared per second squared. And then when I take the square root back two meters per second, the the average speed is just add up all of the values and divide by six. And indeed, the result is close to the root mean square speed on the question asks. Well, why is the root mean square speed always larger and essentially in taking the squares? Uh, before you divide by six when you take that average. In essence, each of the values has been weighted by itself and said the larger values, uh, 3.5 is multiplied by 3.5, but to is only multiplied by two And so it&#x27;s as if where it is actually that the greater values are weighted more, they essentially count more, and so the overall average is going to be greater.

Christopher Dzorkpata · Answer

Hello. So, for the first part of this problem, I&#x27;m going to write down the expressions we need to make the analysis. So the, uh, average kinetic energy, the average kinetic energy my gas were given by three over to 33 Que is the Bozeman Constant T is the temperature the Richmond square speed Also given by three. Okay, t over him. So, uh, if we compare these two equations So for the kinetic energy, the 3/2 it&#x27;s a constant Goldsman constant. It&#x27;s a constant. So what it means is that it can. Attic energy really depends on the temperature. So from the question, because the temperature is the same, what it means is that a k e the average translation of candidate energy is the same because the temperature is the same and the clinic energy depends on Lee on the temperature. So the ship now you go to the root mean square speed. He realized that the it depends on the temperature and the mosque. So for the temperature side, it&#x27;s okay, but for the mask. So we look at the masters off a and B, they&#x27;re different. And the way we look at the relationship between the V. R. M s and the mosque. It&#x27;s an inverse relationship. What it means is that if you have a lot of molecules, we&#x27;re gonna have a very high um v RMS So when you look at the mask A and B Iran is that, um a it&#x27;s lighter than be so what it means is that mhm we&#x27;ll have a higher Aramis don&#x27;t be. And so we&#x27;re selling because, uh, the mass off a is smaller than the mass off B. Then A is gonna have a high v rms than be so so the VR mess. So still on the ape are the V Arabs. Oh, okay, is greater than the V rms off the So let&#x27;s go to the be part for the be part we wanna know. So giving this condition, we want to know which of the temperatures should we raise so that they become equal. So, like I said, the mouth off a it&#x27;s lighter that it must be. And so if you want to raise any temperature, then he&#x27;s got to be be because the question is asking that we want to raise the temperature for one of them. So that they have the same via Aramis. So if you want to raise the temperature off any of the continent so that the proms is at the same So here you see the pop. Now, the Viramontes off a is greater than the very famous off B. So if you want the firearms to be equal now, you want to increase the, uh, temperature off the so for the deep part, you&#x27;re going to raise temperature off so that they can have the same the arms you can see. So foresee. Let me check the question again quickly. So for C, we want to know the temperature at which will accomplish this. Go. All right. So let&#x27;s go back to V arms formula. Um, our mus of course. Uh, three Q t over him. Okay, so we wanna make sure that the proms off a It&#x27;s a quoted the virus off B. So we wanna find that temperature, and that&#x27;s accomplished that. So I can see. But the V arms off the, which is three Katie over eight should be equal to the V arms off being, which is also a quote to three. Katie over there will be empty on the So we are quitting them. So we&#x27;re gonna have Is three Katie a spirit thio? I&#x27;m a actually, we could too. Yeah, so that&#x27;s c a a temperature off. And, um is that three? Katie. Oh, Harambe. So what we&#x27;re gonna do is I&#x27;m gonna try and, uh, isolated t and the M because the trade K are all constants, so I don&#x27;t need them. So what I&#x27;m gonna do is this, um I&#x27;m gonna see okay through three k times t a over me. The same thing. Three key a square root price T B over Andi. That should be so that this can cancel that the alcohol fruits t a over a really good too. Square it off TV over and be We can square both sides of the equation to get rid off the right side. So you have to see over a So this is may o t. P over on b. So we&#x27;re trying to find is we&#x27;re trying to find t. B. So I started TV No ta for me times and beat. Okay. I&#x27;m gonna go ahead and do my substitution. I see a 20. Just a second. Um, that will be 10 degrees. So, 10 we gotta change that. Calvin. So 10 degrees, um, plus 2 +73 Divided by the mask off a 3.34 3.34 I turned to the negative 27 on the mouth of P 5.34 5.34 that the minus 26. So the temperature off B Children should be four point 53 I tend to the third covering. So this it&#x27;s, uh, the amount of temperature he needs to get to in order for them to have the C Pharma&#x27;s in the last part is it be? They want to know which molecules would not have the greater average clinic energy the molecule. So that&#x27;s the last part. The now the temperature off B is greater than the temperature off a. So that means that in molecules in B who have a greater kinetic energy per molecule because, like I said, let&#x27;s go back. The kinetic energy depends on Lee on the temperature, so know that we have t B to be. This temperature is going to be higher than the temperature off a. So the average kinetic energy off B is going to be higher than E just because of the temperature. So the temperature off B is now greater Now the temperature off a so the molecules in B will have a greater kinetic energy per molecule. Yeah, off the cells. Thank you.

Problem 97 Hard Difficulty

Answer

4.71

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