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(I) If you double the mass of the molecules in a gas, is it possible to change the temperature to keep the velocity distribution from changing? If so, what do you need to do to the temperature?

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Double the temperature.

Physics 101 Mechanics

Chapter 18

Kinetic Theory of Gases

Temperature and Heat

Cornell University

University of Michigan - Ann Arbor

University of Washington

Hope College

Lectures

01:01

What temperature change wo…

01:19

Can the speed of a given m…

01:31

01:26

A gas is at $0^{\circ} \ma…

01:17

Is it possible to decrease…

01:36

If the translational speed…

02:01

01:41

CE If the translational sp…

01:13

An ideal gas is at a tempe…

01:30

Suppose you double the tem…

Okay, so we're doing Chapter 18 problem light. So it says if you double the mass of the molecules and gas also mass goes to to mass. Is it possible to change the temperature to keep the velocity distribution for, say, staying from changing. Okay, So what is the velocity distribution that's given by the Maxwell Holtzman distribution? And this is equated 18.6 in the book. If you're curious, it was kind of complicated here so that all right, it bounces four pi times in times in over to pie. Okay. Beaty to the three house B squared E to the negative one, huh? In the squared. Over. Okay, beauty. Cool. So we want this to be the same. So are in is going to two, and we want to know. Can we change borrower t temperature toe? Make sure this is always the same. Whoa. If we look at this equation whenever we see an end, it always comes in the form of em over tea and to see that weaken. Let's call this in variable X. And I can rewrite this right. So half of the is now or pie and times x over two pi k b to the three house the squared E to negative 1/2 these squared X over, kid Be so weakens. Combine M and T until one very border and nothing changes in our equation. So it in over t stays constant. Then we're good. So that means I am going to two n over what equals and over teeth. Right? And you should see this is simply just the question mark must be to t. So if we double the mass and double the temperature at the same time, our distribution is going to say the same. Well, it's gonna be constant awesome.

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