# Differences

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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] 2015/11/11 08:54 mdawber [Using the Ideal Gas Law to determine Absolute Zero] 2015/11/06 09:08 mdawber [Ideal Gas Law] 2015/11/06 09:01 mdawber [Thermal Stress] 2015/11/06 09:00 mdawber [19.P.014] 2015/11/06 08:50 mdawber [Thermal Expansion] 2015/07/22 11:47 mdawber [Thermal Stress] 2015/07/22 11:46 mdawber [What makes a gas ideal?] 2015/07/22 11:46 mdawber [Thermal Stress] 2015/07/22 11:43 mdawber created Next revision Previous revision 2015/11/11 08:54 mdawber [Using the Ideal Gas Law to determine Absolute Zero] 2015/11/06 09:08 mdawber [Ideal Gas Law] 2015/11/06 09:01 mdawber [Thermal Stress] 2015/11/06 09:00 mdawber [19.P.014] 2015/11/06 08:50 mdawber [Thermal Expansion] 2015/07/22 11:47 mdawber [Thermal Stress] 2015/07/22 11:46 mdawber [What makes a gas ideal?] 2015/07/22 11:46 mdawber [Thermal Stress] 2015/07/22 11:43 mdawber created Line 70: Line 70: 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 ===== Line 100: Line 106: 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. + +