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 24

Q

A

$1.0 \times 10^{3}{}^\circ \textrm{C}$

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VIDEO TRANSCRIPT

This is Giancoli Answers with Mr. Dychko. Initially in the cylinder you have some initial pressure atmospheric pressure, *p1*, times some initial volume, *v1*, which we don't know. And it equals the number of moles of the gas in there times the universal gas constant times the initial temperature expressed in kelvin. And then after the compression happens. You have some new pressure *p2* times some new volume *v2* equals *n R* times *t2*. And this *n* does not have a subscript because it's the same molar quantity of gas in both cases. So, *n R* is *p1 v1* over *t1* if you divide both sides of this by *t1*. And then we can substitute this in place of *n R* in the second formula. So, we have *p2 v2* equals *p1 v1* over *t1* times *t2*. And then we can solve for *t2* by multiplying both sides of this by *t1* over *p1 v1*. And the *p2 v2* gets multiplied by *t1* over *p1 v1*. And the *t2* gets isolated and we switch the sides around. And so the temperature after compression is going to be the initial temperature, 20 degree Celsius plus 273.15 to convert it into kelvin times 40 atmospheres after compression, *p2*, times the new volume which is 1/9 times the initial volume and divide that by the initial pressure of 1 atmosphere times the initial volume, *v1*. The *v1's* cancel. And this works out to 1302.89 kelvin. And if you take away 273.15 we can write this in Celsius. And this kind of explains why diesel engines don't need spark plugs because after compression the temperature is so high that this can ignite a diesel fuel just as a result of the temperature increased because of compression.

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