Young/Freeman University Physics 11e

Ch 18 Thermal Properties of Matter © 2005 Pearson Education

18.1 Equations of State Total mass, number of moles, and molar mass Ideal-gas equation © 2005 Pearson Education

An improvement to the equation of state The van der Waals equation includes corrections for the facts that molecules are not point particles, that they have volume, and for the attraction/repulsion that naturally exists between the adjacent atoms/molecules in an ensemble. The van der Waals equation includes corrections for the facts that molecules are not point particles, that they have volume, and for the attraction/repulsion that naturally exists between the adjacent atoms/molecules in an ensemble.

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18.2 Molecular Properties of Matter © 2005 Pearson Education

molar mass, Avogadro’s number, and mass of a molecule © 2005 Pearson Education

18.3 Kinetic-Molecular Model of an Ideal Gas © 2005 Pearson Education Elastic collision of molecules

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The distribution function satisfies the normalization relation The total momentum change due to the collisions is

From the definition of Pressure

Example: Please estimate the root mean square mean velocity of Hydrogen gas. A. 2000B. 1000C. 500 E. 250D. 100 m/s

Average translational kinetic energy of moles of ideal gas Average translational kinetic energy of a gas molecule Root-mean-square speed of a gas molecule © 2005 Pearson Education

18.4 Heat Capacities Ideal gas of point particles © 2005 Pearson Education

Diatomic gas, including rotation © 2005 Pearson Education

Ideal Monatomic Solid © 2005 Pearson Education Rule of Dulong and Petit

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18.5 Molecular Speeds © 2005 Pearson Education

From thermodynamic, the probability of a particle stay in an energy state of E is proportional to Use the mathematical property where

H.W. Find average velocity and most probable velocity.

Maxwell-Boltzmann distribution © 2005 Pearson Education

mean free path of a gas molecule © 2005 Pearson Education Collisions between Molecules

二項分佈 (Binomial Distribution) 若執行 N 個統計上獨立的試驗，而每個試驗只有兩種 不同的結果之一 ( 如 +1 與 -1 或 0 與 1 等 ) ，令其中之一結 果 ( 如 +1) 的可發生機率為 P ，而另一結果為 q ，則應滿 足 p+q=1 。 由數學上二項式的展開式結果，我們可得上述機率分 佈歸一化的結果

對於產生 +1 結果次數的期望值為 二項分佈的變異數可由定義 而其標準差則為

常態分佈 ( 高斯分佈 )(Normal or Gaussian Distribution) 上述的二項分佈中，若 N 值非常大，則其分佈於 p=q 時接近於所謂的常態分佈，又稱高斯分佈。數學上可 寫為

大氣層的壓力會隨高度升高而下降。這是因為位 於地表上的空氣會被其之上的所有空氣壓著，反 之在高的地方，空氣被少一點的空氣壓著，故之 氣壓亦隨之遞減。氣壓隨高度而改變是可以根據 下列的流動動力學程式所計算：流動動力學

18.6 Phases of Matter © 2005 Pearson Education

Temperature ( o C) Vapor Pressure (Pa) Dew Point