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Unformatted text preview: 2.57 Nano-to-Macro Transport Processes Fall 2004 Lecture 2 5.1 Heat conduction T h T c In last lecture, we describe electrons as free electron gas and lattice vibrations as phonon gas. Basically they are both gases in a box. 5.2 Convection 1) Typically electron velocities are 10 5-10 6 m/s, while phonon velocities are the sound velocity. G 2) In heat conduction processes, the average velocity of heat carriers is v = 0. In convection, a non-vanishing average velocity superimposed on their random G velocity, resulting in v . 3) When a liquid or gas molecule is moved from one place to another due to its nonzero velocity, it also carries its internal energy. 5.3 Radiation 8 6 1 / 900 10 3 c f = = = at frequency h . E 2 E 1 E= nh 1) Wavelength comparison For radio/TV signals, we get 3 10 (m), where we use 900 MHz as the frequency. This wavelength is still much larger than that of the thermal radiation (around 0.5 m). 2) Generation of thermal radiation Thermal radiation typically refers to the electromagnetic waves that are generated by the oscillation charges in the atoms and crystals, while TV and radio signals are generated by artificial current oscillation in a circuit. An electromagnetic wave can only have energy that is multiple times of Emission 2.57 Fall 2004 Lecture 2 1 5.4 Pressure and shear stress x As is shown in the figure, the velocities of gas molecules distribute randomly in all directions. Pressure is caused by their momentum changes normal to the wall. For one molecule, we have G G G d mv ) or F = m v x > 0 v ) m v ( ( = x < 0 = x F ma = . x dt t t Denote n [m-3 ] as the number of particles per unit volume. We notice nv x [m-2 s-1 ] has the physical meaning as the flux of particles on the wall. Assuming elastic collisions between the wall and molecules, we have v = 2 v > . Thus x x 0 2 P = 1 2 n v x > ( m v x ) = m n v x 2 > 0 = m n v x = m n v 2 , 3 2 2 in which we use average v 2 = v + v y 2 + v = 3 v 2 . From here, you can derive the ideal ....
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- Fall '04