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 34

Q

A

$V_2 \textrm{ is } 1.4 \textrm{ times } V_1$

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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. When the helium balloon is in the child's hand, the pressure is an atmospheric pressure, *P1*, and it has some initial volume, *V1*, and that equals *n*, the number of moles of air inside the balloon times the universal gas constant times the temperature at sea level. And we can divide both sides by *T1* and get *P1 V1* over *T1* is *n R*. And then when the balloon is way up in the atmosphere, there's still gonna be the same number of moles of gas in it, but there's gonna be a different pressure, different volume and a different temperature. And so we have *P2 V2* over *T2* is the same *n R* but since both of these equal and *n R*, they're equal to each other and so that's what we write here. And then we can solve for *V2*, multiply both sides by *T2* over *P2*. So, *V2* is *T2 P1 V1* over *P2 T1*. And comparing it to the initial volume, good way to compare it is to divide it maybe and see what the fractional changes. And so that *V2* over *V1* is *T2 P1 V1* over *P2 T1*, that's what volume 2 is. And divided by *V1* which is the same as multiplying by 1 over *v1*. *v1's* cancel and that means the fractional change in volume is temperature up in the atmosphere times the pressure at sea level divided by the pressure way up in the atmosphere times the temperature at sea level. So, temperatures have to be converted into kelvin. 5 degrees Celsius plus 273.15 gives the temperature in kelvin in the upper atmosphere times 1 atmosphere pressure at sea level divided by 0.68 atmospheres of pressure way up there times 20 degrees Celsius plus 273.15. And that gives about 1.4. So, *V2* is 1.4 times *V1*. So, the volume of the balloon up in the atmosphere in the sky is 1.4 times what it was at sea level.

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