the-most-probable-speed-of-the-molecules-in-a-gas-at-temperature-t_2-is-equal-to-the-rms-speed-of-th

Question

The most probable speed of the molecules in a gas at temperature $T_{2}$ is equal to the rms speed of the molecules at temperature $T_{1}$ .
Find $T_{2} / T_{1}$ .

Michael Mackenzie · Accepted Answer

So we&#x27;re given that the bomb Most probable velocity at T two equals the room being squared. Velocity that t one So the P equals the square root to Artie over M and V. Arma equals swear. Rule of three. Artie over M. So the ratio of these two the p over proms a T one here T to here equals one because they were equal equals. Here are an M. We&#x27;ll cancel in our ratio, so we&#x27;ll get the square root. Two King two over square, room three. Okay, one So we can square one. And this will give us two tea too. Over three. One equals one. Which gives us tea, too. Over t one equals three over too.

Sanjeev Kumar · Answer

As for the given caution, we are provided with the temperature that is equal to 2 96 Calvin. Most probable speed that is equal to re M P is equal to 2 63 meter per second. We have to calculate the molar mass off the given compound for that. As we know most probable spirit is equal to the square root off to rt over um, squaring both side We get the result. We square am p is equal toe to Artie over. Um, from here we get the result off Moeller mus as to rt over the square Ambi By substituting all the values in it, we get to into 8.314 as our is universal guest constant and temperature that is, to 96 over most probable speed that is to 63 square. So by soldering this we get the result 0.7 double 157 Grandpa sex, which is the required result off the molar mass for the caution

João Gabriel Alencar Caribé · Answer

in this question. We want to increase the temperature of aghast such that the new RMS speed is 1% bigger than the old Armas speed. That is the new aroma. Speed is them when 101% off the old are a massive speed. The old RMS speed can be written as follows. V R. A mass is equals to the square. Root off three times skate times the old temperature. Remember to always convert to Calvin&#x27;s. Then we have 20 blows, 273 to convert from cells is to calving. All we have to do is add 273. Then we divide it by the mass off each Moya coup. And now, after heating the gas, the new Artemus Speed V prime are mass is given by the square it off three times Key times T prime divided by the mass and now use this equation. We know that the prime are a mass showed square root off three timescale times T prime divided by the mass Easy close to 101%. There is 101 divided by 100 off the own Azamat speed off three time ski times 293 divided by the mass off each Moya coup. Then we square both sides off this equation. So we have three times k. I&#x27;m Steve Prime, divided by the mass over that inside and 101 divided by 100 squared times. Three time skate times 293 divided by the mass in the right. Inside. Now it&#x27;s simplified, the common terms off three Okay and M and end up with an expression 40. Prime, which is steep. Prime, is 101 divided by 100 squared times 293. And these results in T prime equals truth. True lying 88 893 divided by 10,000 Calvins. But we want the temperature in Celsius. In order to convert this temperature from self Calvin two Celsius, we have to subtract 273 from it. Then we have true 988 893 divided by 10,000 minus 273. And these results in a temperature approximately 25 0.9 degrees cells. India&#x27;s Is that sort of this question

João Gabriel Alencar Caribé · Answer

we have a gas at 20 degrees Celsius and it has some RMS speed v r m s. We went toe hit that gas to some temperature T prime. Such that V prime are a mass physical security kinds. We are a mass, so we want to heat it such that the new army speed is two times bigger than the old are amassed speed. For these questions, we can use this equation, which tells us the relation between the RMS speed on the temperature. So before heating the RMS Speed Waas week are a mess equals to the square it off three times Kate times the temperature which we should always convert to Calvin&#x27;s from cells use to Calvin&#x27;s You just have to add 273. So this is 20 plus 273 divided by the mass off each Moya coup. Then this is the square it off three times, Kate Times 293 divided by the mass and these waas the RMS speed before hitting after heating. We have an argument Speed V Prime R M s that is given by the square root off three times Cape time steep prime divided by the mass but feet prime RMS must Lee goes to truth times v r m s. But we know that v R M s is the square root off three times skate times 293 divided by the mass. So we have a new equation with three times skate times t prime divided by em on the left hand side and two times the square root off three times Skate times 293 divided by AM on the right hand side now is square Both sides off this equation to get three time scape time. Steep price divided by M is equals to four times three time ski times 293. Do you find it by the Mass? Now we have a lot of simplifications happening. We can simplify the man&#x27;s with the mass boatman Constant with boats Man Constant three Street and were last with the prime. So t prime is equals to four times 293 and that is 1172. Calvins, which is equivalent troop 1172 miners 273 cells years on. These is 899 degrees Celsius, and this is the answer to this question.

Mihajlo Grcic · Answer

So first, to find the maximum off some function, we will need to set the derivative of that function to be able to zero and then solve that is the differential equation to find the bathroom that we&#x27;re looking for In this case, we toe first determine what function we need. We need to function that shows the distribution on the number of particles per speeds. Travelocity&#x27;s and this is Max very in lasted velocity distribution. So it looks like and oh, velocity and then some differential, the lost internal that is equal. Jewell, This is the textbook formal de jure formula. It was already the ride both my constant absolute temperature team again, both midcoast intensity spends nearly So this is the number off particles that will take the gases from we to TV. So this is the infinite decimal. Terrible off lasts and we need to set this function here. So the end off we over the lead must be put zero. So I would see what that means. That means that you need to take the river to off off the whole function. So basically the over the be so the derivative over velocity off this function this very. But you must be equal to zero. So well, take to the river to off each and every parts. And then we&#x27;ll set it to zero and find the resulting equation for their lost moves from constant here. And this is equal to zero. So we should see that most of the terms here constant and they&#x27;re not functions of the lost. Its only only this part here is the function off the last, and we can reduce searching for for the derivative by dividing both sides. By this constant term, since one side zero, it could stay zero. But on the left can side Look, I&#x27;m a simpler for which will be We can do this any time that we have some function time so constant that must be equal to zero. And the real deal that function basically only these red part of the expression is dysfunctional part Now the derivative of this we&#x27;ll do it in in alliance with the loss off the relation. So first the derivative with square times new spark Then they would you off this part times we squares and then on the anti stood together. So it will be until we, Which is the reality of the square times eternity, um, squared over two, both from costs and stand did plus we square times than the river to the expression of function and the nest function in the exponential, which is also function off the last. So it will be two times, um, velocity. Well, it&#x27;s been caused the temperature just cancel out and then the explosion function itself exponential functional. This state&#x27;s after the dead innovation. Okay, so, again, this and this we can divide both sides with with disturbs and me the pleasure And we will they obtain a much simpler form is equal to zero factor relative velocity. So be we squared show here since we should you turn it our because of just on also will arrays This raises students since that this mistake most men costs and times temperature all of this sequence to zero. So one of the solutions of this equation clearly that we zero but this is a criminal one. So the search for the other solution which stays that this term inside must be zero on In that case, basically, this means that minus sign right inside and over Bozeman&#x27;s Costin&#x27;s time t is. He puts on anything to, in this case, this term zero. So here we can move this part the right hand side. And also remember, this is the maximum velocity I see. This is minus and this is minus. It will be positive. So both Mickelson&#x27;s times temperature over mess times to and from here clearly to see that it&#x27;s squaring stuff, which is the proper form. I hope you find these helpful and they hope to see you in another lesson.

Christopher Provencher · Answer

okay. In this problem, we have ah, gas. 20 degrees Celsius. We want to raise it, root me and square velocity by 2% and were asked to find what temperature Where we have to raise this gas to in order to raise its arm s velocity by 2%. So in order to raise our DVR mess by 2% were really saying Is that v R m s too? This is after we raise the temperature over V. R. M s one its initial our mess. This ratio must be equal to 1.2 That would be 2% increase. So at this point, we can plug in the formula. Next. The simple expression for what? The V r messes in terms of temperature and mass of our gas. We&#x27;ll be left with square root of three Katie to the temperature after over M. And that&#x27;s over. Three Katie one over him. So for something, it&#x27;s the same gas massive. The same cases aim or three is the same. They&#x27;re all gonna cancel out, and we&#x27;ll be left with fruity to over t one. Thus, it must be the case that t two equals t one times 1.2 squared. Okay, so at this point, we could simply plug in R T one and Kelvin to find T, too. So when Kelvin 20 degrees is 293 degrees but 15 we just moved by that by 1.2 squared, our final answer would be 31. Well, what&#x27;s what&#x27;s express it in Calvin. First it would be 305 Kelvin, which is also 31.8 Celsius, and that&#x27;s it.

Problem

Figure $19-23$ shows a hypothetical speed distrib…

Problem 36 Easy Difficulty

The most probable speed of the molecules in a gas at temperature $T_{2}$ is equal to the rms speed of the molecules at temperature $T_{1}$ .
Find $T_{2} / T_{1}$ .

Answer

$\frac{T_{2}}{T_{1}}=\frac{3}{2}$

Related Courses

Fundamentals of Physics

Related Topics

Discussion

Top Physics 101 Mechanics Educators

Christina K.

Marshall S.

Farnaz M.

Jared E.

Physics 101 Mechanics Courses

Math Review - Intro

Algebra - Example 1

Recommended Videos

Watch More Solved Questions in Chapter 19

Video Transcript

David Halliday, Robert Resnick , Jearl Walker

Fundamentals of Physics

Christina K.

Marshall S.

Farnaz M.

Jared E.

Math Review - Intro

Algebra - Example 1

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{T_{2}}{T_{1}}=\frac{3}{2}$

Fundamentals of Physics

Christina K.

Marshall S.

Farnaz M.

Jared E.

Math Review - Intro

Algebra - Example 1

David Halliday, Robert Resnick , Jearl WalkerFundamentals of Physics

Christina K.

Marshall S.

Farnaz M.

Jared E.

David Halliday, Robert Resnick , Jearl Walker

Fundamentals of Physics