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 42

Q

A

$7.3 \times 10^{-4}$

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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Pressure times the volume of the gas equals the number of molecules times Boltzmann's constant times the temperature. And we can divide both sides by the pressure to get the volume of the gas *N K T* over *P*. Now, the volume occupied by the molecules themselves is going to be the number of molecules times the volume of 1 molecule volume per molecule. So, and we're told the volume per molecule is *l naught* cubed. And so to find the fraction of the total volume that the molecules take. We'll take volume of the molecules divided by the volume of the gas. And so that's an *l naught* cubed, volume of the molecules, divided by *V* gas but we'll multiply it by its reciprocal. So, multiply it by *P* over *N K T*. And the *N's* cancel which is good because we don't know how many molecules were dealing with. And we have *l naught* cubed times pressure over *K T*. And we have to assume standard temperature and pressure. So, that means we have 0.3 nanometers and nano is times 10 to the minus 9. So, we have 0.3 times 10 to the minus 9 meters cubed times 1.013 times 10 to the 5 pascals atmospheric pressure divided by 1.38 times 10 to the negative 23 joules per kelvin, Boltzmann's constant times 273 kelvin, standard temperature. And that gives 7.3 times 10 to the minus 4, that's the fraction of the volume of the gas volume that's occupied by the molecules themselves. So, gases are mostly empty space. So, the molecules account for about 0.07% after you multiply this by 100 to turn it into a percent, 0.07% of the volume of the gas is occupied by the molecules themselves.

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