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 63

What is the mass of water in a closed room 5.0 m×6.0 m×2.4 m5.0 \textrm{ m} \times 6.0 \textrm{ m} \times 2.4 \textrm{ m} when the temperature is 25C25 ^\circ \textrm{C} and the relative humidity is 55%?

0.91 kg0.91 \textrm{ kg}
Giancoli 7th Edition, Chapter 13, Problem 63 solution video poster

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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.

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