Giancoli 7th Edition textbook cover
Giancoli's Physics: Principles with Applications, 7th Edition
Temperature and Kinetic Theory
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13-1: 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 41

The lowest pressure attainable using the best available vacuum techniques is about 1012 N/m210^{-12} \textrm{ N/m}^2. At such a pressure, how many molecules are there per cm3\textrm{cm}^3 at 0C0 ^\circ \textrm{C}?

300 \textrm{ molecules/cm}^3
Giancoli 7th Edition, Chapter 13, Problem 41 solution video poster

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This is Giancoli Answers with Mr. Dychko. P V equals the number of molecules times Boltzmann constant times temperature and we can solve this for N over V by dividing both sides by V K and T. So, we have pressure over K T because the v's cancel, equals the number of molecules divided by the volume and because the K T cancels here. And that's 10 to the minus 12 newtons per meter squared lowest attainable pressure, and then divided by Boltzmann constant 1.38 times 10 to the minus 23 joules per kelvin times the standard temperature of 273.15 kelvin. And this is going to give us number of molecules per cubic meter, and so we have to convert that into per cubic centimeter, because that's what the question asks us for, by multiplying by 1 meter for every 100 centimeters, cubed, and we end up with about 300 molecules per cubic centimeter.

By bmalan on Wed, 7/29/2020 - 4:39 AM

Hello Mr. Dychko, I am not sure how but every time I plug this into my calculator I get 2,652 instead of 265.2.

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