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 63

Q

A

$0.91 \textrm{ kg}$

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

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. We're gonna figure out the mass of water in this room by first figuring out the number of moles of water from this ideal gas law. And we can divide both sides by *R T*. And we get number of moles is the pressure times the volume divided by ideal gas constant times temperature in kelvin. And the mass of water will be the number of moles multiplied by the molar mass of water. And so that's *P V* capital *M* over *R T*. So, the only thing we don't really know straight off the bat is the pressure and we can figure it out, though, because humidity is partial pressure divided by saturated vapor pressure at that temperature. And so the pressure is the pressure due to the water itself, partial pressure. So, partial pressure is humidity times saturated vapor pressure at that temperature. And so that means the pressure is 0.55 times the saturated vapor pressure at 25 degree Celsius which we find in this table, 13-3. And reading it off, it's 3.17 times 10 to 3 pascals. And we multiply by the volume of the room, multiplying the dimensions together times by the molar mass of water which is 2 times the molar mass of hydrogen and then plus 1 oxygen, and that's in grams per mole, so we multiply by 10 to the minus 3 to make it kilograms per mole. And divided by 8.314 joule per mole kelvin and times by the temperature of 25 degrees Celsius converted into kelvin by adding 273.15. And we get 0.91 kilograms is the total mass of all the water vapor.

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.