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 45

Q

A

$1.2$

In order to watch this solution you need to have a subscription.

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. We're going to divide the two rms speeds in order to see by what factor they change when the temperature changes. So, the rms speed of the first temperature is going to be square root of 3 times Boltzmann's constant times the first temperature, *T1*, over the mass of a single molecule. And then the rms speed in the second case is going to be the same formula with *T2*, it's the same molecule, so it's the same mass there. So, our *V rms2* divided by *V rms1* is *V rms2* multiplied by the reciprocal of *V rms1* instead of dividing by a fraction of multiplying by its reciprocal, so, that's way you see square root *m* over 3 *K T1* here. And the *m's* cancel the square root of 3 *K's* cancel and we're left with square root *T2* over *T1*. These temperatures have to be written in kelvin, as always, for these formulas. So. That's square root 160 degrees Celsius plus 273.15 divided by 20 degree Celsius plus 273.15. And that gives about 1.2 is the factor by which the rms speed changes when the temperature changes from 22 degrees Celsius to 160 degree Celsius.

Giancoli Answers, including solutions and videos, is copyright © 2009-2024 Shaun Dychko, Vancouver, BC, Canada. Giancoli Answers is not affiliated with the textbook publisher. Book covers, titles, and author names appear for reference purposes only and are the property of their respective owners. Giancoli Answers is your best source for the 7th and 6th edition Giancoli physics solutions.