lec7_2011 - Chapter 21: Molecules in motion Diffusion: the...

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Chapter 21: Molecules in motion Diffusion : the migration of matter down a concentration gradient. Thermal conduction : the migration of energy down a temperature gradient. Electric conduction : the migration of electric charge along an electrical potential gradient. Viscosity : the migration of linear momentum down a velocity gradient. Effusion : the emergence of a gas from a container through a small hole.
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21.1 The kinetic model of gases Three assumptions: 1. The gas consists of molecules of mass m in ceaseless random motion. 2. The size of the molecules is negligible, in the sense that their diameters are much smaller than the average distance traveled between collisions. 3. The molecules interact only through brief, infrequent, and elastic collisions. ( Elastic collision : a collision in which the total translational kinetic energy of the molecules is conserved.)
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Pressure and Molecular speeds PV = 1/3 nMc 2 (21.1) where M = m N A , the molar mass of the molecules, c is the root mean square speed of the molecules: c = < v 2 > 1/2 (21.2)
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Relationship between the temperature and the root mean square speed Provided that the root mean square speed of the molecules depends only on the temperature: pV = constant at constant temperature In comparison with Boyle’s law, one gets c = (21.3) The root mean square speed of the gas molecules is proportional to the square root of the temperature and inversely proportional to the square root of the molar mass. 2 / 1 3 M RT
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Maxwell distribution of speeds (21.4) Fraction in the range v 1 to v 2 equals 2 1 v v dv v f ) ( RT Mv e v RT M v f 2 / 2 2 / 3 2 2 4 ) ( - = π
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Expression of molecular speeds Mean speed = The most probable speed Relative mean speed: (reduced mass) - c 2 / 1 8 M RT π 2 1 2 / * = M RT c 2 1 2 1 8 2 / _ / _ = = π μ kT c c rel B A B A m m m m + = μ
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Measuring molecular speed
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Molecular motion in gases PV = 1/3 nMc 2 (21.1) where M = m N A , the molar mass of the molecules, c is the root mean square speed of the molecules:
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This note was uploaded on 02/14/2011 for the course SCIENCE 321 taught by Professor Aaa during the Spring '11 term at Windsor.

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lec7_2011 - Chapter 21: Molecules in motion Diffusion: the...

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