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phy131studiof15:lectures:chapter19 [2015/07/22 11:43] mdawber created |
phy131studiof15:lectures:chapter19 [2015/11/11 08:54] (current) mdawber [Using the Ideal Gas Law to determine Absolute Zero] |
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Coefficients of thermal expansion can be found [[http://en.wikipedia.org/wiki/Thermal_expansion|here]] or your textbook. | Coefficients of thermal expansion can be found [[http://en.wikipedia.org/wiki/Thermal_expansion|here]] or your textbook. | ||

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+ | ===== 19.P.014 ===== | ||

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+ | ===== 19.P.017 ===== | ||

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===== Some Thermal Expansion demos ===== | ===== Some Thermal Expansion demos ===== | ||

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These stresses can be reduced by the inclusion of [[wp>Expansion_joint|expansion joints]] in bridges, roads and pipes. | These stresses can be reduced by the inclusion of [[wp>Expansion_joint|expansion joints]] in bridges, roads and pipes. | ||

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+ | ===== 19.P.025 ===== | ||

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+ | ===== What makes a gas ideal?===== | ||

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+ | There are a number of conditions which must be satisfied for a gas to be considered ideal | ||

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+ | - There must be a large number of molecules and they should move in random directions with a range of different speeds. | ||

+ | - The spacing between molecules should be much greater than the size of the molecules. | ||

+ | - Molecules are assumed to interact only through collisions. | ||

+ | - The collisions are assumed to be elastic. | ||

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+ | ===== Boyle's Law ===== | ||

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+ | At constant temperature, it is found that the product of the pressure and volume of an ideal gas are constant | ||

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+ | $PV=\mathrm{constant}$ | ||

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+ | This is named [[wp>Boyle%27s_law|Boyle's Law]], after Robert Boyle who formulated it in 1662. | ||

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+ | {{Boyles_Law_animated.gif}} | ||

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+ | ===== Charles' Laws ===== | ||

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+ | Joesph Louis Gay-Lussac published [[wp>Charles%27s_law|Charles' Law]] in 1802, attributing it to unpublished work of Jacques Charles in the 1780's (Gay-Lussac has his own law..though it's not clear he should!). | ||

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+ | Charles' Law states that at constant pressure the volume of a gas is proportional to the temperature. | ||

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+ | $V\propto T$ | ||

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+ | {{Charles_and_Gay-Lussac's_Law_animated.gif}} | ||

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+ | ===== Gay-Lussac's law ===== | ||

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+ | [[wp>Gay-Lussac%27s_Law|Gay Lussac's Law]] states that for a fixed volume the pressure is proportional to the temperature | ||

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+ | $P\propto T$ | ||

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+ | ===== Ideal Gas Law ===== | ||

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+ | The combination of the previous 3 laws implies that | ||

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+ | $PV\propto T$ | ||

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+ | Our previous laws were for systems of constant mass, but we can see that the amount of mass should effect the volume (at a given pressure) or the pressure (at a given volume). | ||

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+ | $PV\propto mT$ | ||

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+ | Measuring the amount of mass in moles will allow us to write the ideal gas law in terms of a universal constant. A mole of gas is a given number of molecules, Avagadro's number, $N_{A}=6.02\times 10^{23}$. If we have a certain mass $m$ of a gas which has a certain [[wp>Molecular_mass|molecular mass]] (measured in atomic mass units, $\mathrm{u}$, which are also the number of grams per mole.), the the number of moles $n$ is given by | ||

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+ | $n=\frac{m[\mathrm{g}]}{\textrm{molecular mass}[\mathrm{g/mol}]}$ | ||

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+ | and | ||

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+ | $PV=nRT$ where $R=8.314\mathrm{J/(mol.K)}$ | ||

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+ | This equation is the [[wp>Ideal_gas_law|ideal gas law]] | ||

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+ | ===== 19.P.034 ===== | ||

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+ | ===== 19.P.042 ===== | ||

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+ | ===== 19.P.044 ===== | ||

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+ | ===== Ideal Gas Law for a number of molecules ===== | ||

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+ | The ideal gas law can also be written in terms of the number of molecules $N$ | ||

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+ | $PV=nRT=\frac{N}{N_{A}}RT=NkT$ | ||

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+ | where $k=\frac{R}{N_{A}}=\frac{8.314\mathrm{J/(mol.K)}}{6.02\times 10^{23}}=1.38\times 10^{-23}\mathrm{J/K}$ is the [[wp>Boltzmann_constant|Boltzmann Constant]]. | ||

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+ | ===== Using the Ideal Gas Law to determine Absolute Zero ===== | ||

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+ | If $PV=nRT$ the absolute zero temperature occurs when $P=0$. In practice most gases will liquefy before this point, but we can measure the pressure of a fixed volume of gas at a couple of reference points and extrapolate down to zero pressure to get an estimate for [[wp>Absolute_zero|absolute zero]]. | ||

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+ | Through laser cooling and molecular trapping techniques it is now possible (but difficult!) for temperatures on the order of a $\mathrm{nK}$ to be achieved. Prof. [[http://ultracold.physics.sunysb.edu/index.html|Dominik Schneble]] produces ultra-cold ($\mu K$) Bose-Einstein condensates in the basement of this building! Prof. [[http://www.stonybrook.edu/metcalf/hmetcalf.html|Hal Metcalf]] was one of the key players in the original development of laser cooling. | ||

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