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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. ​
 +
 +===== 19.P.014 =====
 +
 +===== 19.P.017 =====
 +
 +
  
 ===== 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.
 +
 +===== 19.P.025 =====
 +
 +
 +===== What makes a gas ideal?=====
 +
 +There are a number of conditions which must be satisfied for a gas to be considered ideal
 +
 +  - 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.
 +
 +
 +===== Boyle'​s Law =====
 +
 +At constant temperature,​ it is found that the product of the pressure and volume of an ideal gas are constant
 +
 +$PV=\mathrm{constant}$
 +
 +This is named [[wp>​Boyle%27s_law|Boyle'​s Law]], after Robert Boyle who formulated it in 1662.
 +
 +{{Boyles_Law_animated.gif}}
 +
 +===== Charles'​ Laws =====
 +
 +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​Charles%27s_law|Charles'​ Law]] in 1802, attributing it to unpublished work of Jacques Charles in the 1780'​s ​ (Gay-Lussac has his own law..though it's not clear he should!).
 +
 +Charles'​ Law states that at constant pressure the volume of a gas is proportional to the temperature.
 +
 +$V\propto T$
 +
 +{{Charles_and_Gay-Lussac'​s_Law_animated.gif}}
 +
 +===== Gay-Lussac'​s law =====
 +
 +[[wp>​Gay-Lussac%27s_Law|Gay Lussac'​s Law]] states that for a fixed volume the pressure is proportional to the temperature
 +
 +$P\propto T$
 +
 +===== Ideal Gas Law =====
 +
 +The combination of the previous 3 laws implies that 
 +
 +$PV\propto T$
 +
 +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).
 +
 +$PV\propto mT$
 +
 +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
 +
 +$n=\frac{m[\mathrm{g}]}{\textrm{molecular mass}[\mathrm{g/​mol}]}$
 +
 +and 
 +
 +$PV=nRT$ where $R=8.314\mathrm{J/​(mol.K)}$
 +
 +This equation is the [[wp>​Ideal_gas_law|ideal gas law]]
 +
 +===== 19.P.034 =====
 +
 +===== 19.P.042 =====
 +
 +===== 19.P.044 =====
 +
 +
 +
 +===== Ideal Gas Law for a number of molecules =====
 +
 +
 +The ideal gas law can also be written in terms of the number of molecules $N$
 +
 +$PV=nRT=\frac{N}{N_{A}}RT=NkT$
 +
 +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]].
 +
 +===== Using the Ideal Gas Law to determine Absolute Zero =====
 +
 +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]].
 +
 +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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