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(II) If the pressure in a gas is tripled while its volume is held constant, by what factor does $v_{\text { rms }}$ change?

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$\sqrt{3}=1.73$

Physics 101 Mechanics

Chapter 18

Kinetic Theory of Gases

Temperature and Heat

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

Lectures

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(II) If the pressure in a …

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(II) If the pressure of a …

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(I) By what factor will th…

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If the temperature of an i…

So we're doing Chapter 18 Problem nine here. So it says his pressure in a gas is crippled. Bouts volume held constant. Soapy goes to three p. Well, v stays at the, um, we want to see what by what factor does the our best. So for this gas, we know that ideal ideal gas law should hold meaning that P is proportional to teach people. So Avi stays the same and and in our Constance year, that means p going to three p corresponds to t going toe three t. So if our pressure gets tripled, our temperature also must be tripled. So now we want to see what happens to the R s if pressure is crippled. So the R M s is square root of three K B t over him. So we already said that when pressure is tripled, temperature is trouble. So we want to figure out the ratio here so we can do this. Three. We replace t with three t here. So now we can see that everything should cancel out, and we should be. You left with one over square of three and we divided we. So we took the old value and divided about new value. So if we actually want the actor, which it changes, we want to take the new value over the old values, which then becomes the inverse of this, which is just square root of three often. So that means the ROMs times square root of three is what the r. M s. All right? Three tea. Cool. So square root of three was the factor it raised by

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