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phy131studiof16:lectures:chapter17 [2016/11/16 09:17]
mdawber [Problem 17.50]
phy131studiof16:lectures:chapter17 [2016/11/16 09:27] (current)
mdawber [Using the Ideal Gas Law to determine 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. 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.
 +
 +===== Ideal gas law from a molecular perspective ​ =====
 +
 +We can relate the pressure exerted by an ideal gas on it's container to the change in momentum of a molecule when it strikes the container wall
 +
 +{{kinetictheory.png}}
 +
 +The average force due to one molecule is then 
 +
 +$F_{molecule}=\frac{\Delta(mv)}{\Delta t}=\frac{2mv_{x}}{2l/​v_{x}}=\frac{mv_{x}^{2}}{l}$
 +
 +The net force on the wall will be the sum of the forces from all $N$ molecules
 +
 +$F_{net}=\frac{m}{l}\Sigma_{i=1..N} v_{xi}^{2}$
 +
 +$\frac{\Sigma_{i=1..N} v_{xi}^{2}}{N}=\bar{v_{x}^{2}}$ → $F_{net}=\frac{m}{l}N\bar{v_{x}^{2}}$
 +
 +$v^{2}=v_{x}^{2}+v_{y}^{2}+v_{z}^{2}$ → $\bar{v^{2}}=\bar{v_{x}^{2}}+\bar{v_{y}^{2}}+\bar{v_{z}^{2}}=\bar{3v_{x}^{2}}$
 +
 +$F_{net}=\frac{m}{l}N\frac{\bar{v^{2}}}{3}$
 +
 +$P=\frac{F}{A}=\frac{1}{3}\frac{Nm\bar{v^{2}}}{Al}=\frac{1}{3}\frac{Nm\bar{v^{2}}}{V}$
 +
 +$PV=\frac{2}{3}N(\frac{1}{2}m\bar{v^{2}})=NkT$
 +
 +$\bar{KE}=\frac{1}{2}m\bar{v^{2}}=\frac{3}{2}kT$
 +
phy131studiof16/lectures/chapter17.txt · Last modified: 2016/11/16 09:27 by mdawber
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