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 14

Q

A

$6.59\textrm{ mL}$

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

VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. When this container full of water cools down, both, the container and the water will reduce their volumes as a result of this decrease in temperature. And so the amount of water we can add is going to be the amount by which the water contracts more than the container. So, the amount we can add is going to be the final container volume minus the final water volume. And they both start out with the same initial volume because the container is completely full of the water. So, *v naught* over *v* initial for the water and the container are both the same. So, the final container volume will be the initial container volume, *v naught*, plus the change in the volume of the container and then minus the initial volume of the water plus the change in the volume of the water. And these *v naughts* are both the same to begin with and so they make 0. And we have that the volume we can add is the difference in the change in volumes of the container in water. So, here is the change in volume of the container, the coefficient of volume expansion of the ordinary glass times its initial volume times the change in temperature and then minus the change in volume of the water coefficient of volume expansion for water times *v naught Δt*. And *v naught Δt* are the same, we can factor it out and so we have *β c* minus *β w* times *v naught Δt*. And the coefficient of volume expansion for glass is 27 times 10 to the minus 6 minus the coefficient of volume expansion for water, 210 times 10 to the minus 6. And we can see that the volume of the water is going to decrease more than the volume of the glass, and we can see that based on knowing that the coefficient of volume expansion for water is so much greater. This means that the water volume is more sensitive to changes in temperature because this is a greater coefficient. So, we'll take this difference and multiply it by the original volume of 450.0 milliliters times the final temperature of 200.0 degrees Celsius minus the initial temperature of 100 and that gives about 6.59 milliliters is the amount of additional water we can add, this is the amount by which the water volume decreases more than the container volume.

COMMENTS

By saie.joshi on Thu, 11/24/2016 - 4:42 PM

Why do you subtract the values instead of adding them together? Don't both the water and the glass reduce volume?

By saie.joshi on Thu, 11/24/2016 - 4:43 PM

never mind I got it!

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.