Giancoli's Physics: Principles with Applications, 7th Edition

13

Temperature and Kinetic Theory

Change chapter13-1: Atomic Theory

13-2: Temperature and Thermometers

13-4: Thermal Expansion

13-5: Gas Laws; Absolute Temperature

13-6 and 13-7: Ideal Gas Law

13-8: Ideal Gas Law in Terms of Molecules; Avogadro's Number

13-9: Molecular Interpretation of Temperature

13-11: Real Gases; Phase Changes

13-12: Vapor Pressure and Humidity

13-13: Diffusion

Question by Giancoli, Douglas C., Physics: Principles with Applications, 7th Ed., ©2014, Reprinted by permission of Pearson Education Inc., New York.

Problem 49

Q

A

$\sqrt{3}$

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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. We can use the ideal gas law with temperature and pressure are changeable. The number of moles and the volume are not gonna be changing because we're told that its volume is held constant and it doesn't mention that the container is sealed but that's just assumed. So, the number of moles will not change either. So, we can solve this for *T* by dividing both sides by *n R*. And *T* in the first case going to be *P1 V* over *n R*. And *T* in the second case will be *T2* is going to be *P2* over or times *V* over *n R* and *P2* we're told is 3 times the first pressure. So, the second pressure is 3 times the first pressure. So, we have 3 times *P1 V* over *n R* but *P1 V* over *n R* is *T1*. So, we'll substitute that in so, *T2* is 3 times *T1*. And V rms in the first case is going to be square root of 3 *K* temperature 1 divided by *m* and *V rms* in the second case is the same thing with the *T2* instead of *T1*. And we divide them to find the factor by which they are different. And so that means 3 *K T2* over *m* square rooted multiplied by the reciprocal of *V rms1*. So, multiplied by *m* over 3 *K T1* square rooted which gives a bunch of things cancelling. And square root *T2* over *T1*. So, the factor by which the rms speed and the case 2 is different from the rms speed in case 1, is square root of 3 *T1* because that's what we figured out from this ideal gas law that *T2* is 3 times *T1* when you increase the pressure by 3 times while holding volume constant. And the *T1's* cancel. And we're left with square root of 3.

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