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 30

Q

A

$313^\circ\textrm{C}$

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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Because we have a sealed metal container we know that the *n* is going to be constant because it's sealed. And since the container is metal, it's rigid. And so *v* is constant as well. And we don't need any subscripts on these for the two scenarios. So, at the first pressure we have *p1* times *v* equals *n R T1*. And then when the pressure is increased to 2 atmospheres, we have that second pressure times the same volume equals the same quantity, same number of moles of gas times *r* times a different temperature, *t2*. And we can rearrange this to solve for *t2* and by dividing both sides by *n R*. And we get *t2* is *p2* over *v*, *p2* times *v* over *n R*. And then from here, we can see that *v* over *n R* is *t1* over *p*. If you take this and divide both sides by *p1 n R*, you end up with *t1* over *p1*. And then it also equals *v* over *n R* on the other side. So, *v* over *n R* is *t1* over *p1* based on this first equation. And that gets substituted into the second equation, replacing this with *t1* over *p1*. So, *t2* is *p2*, from here, times *t1* over *p1* because that's what *v* over *n R* is. And that's 2 atmospheres times the temperature in kelvin, 28 degrees Celsius plus 273.15. And divided by the original pressure of 1 atmosphere. And that gives 286.3 kelvin. And minus 273.15 to get the answer in degrees Celsius of 313.

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