DThurSep04

# DThurSep04 - Thermodynamics Coldest Place on Earth 1...

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1 Thermodynamics Coldest Place on Earth

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2 Viscosity u+ λ du/d x u u λ
3 Almost the last bit about Viscosity If each plane is of unit area and the molecules move u meters in unit time then the volume of the dotted figure is u m 3 . If there are N molecules in a volume V, then there are Nu/V molecules in the box. Half the molecules are moving up and half down, so the number that cross unit area in unit time is Nu/2V. The momentum transported in unit time is then: dx u d V m u N 2 λ

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4 The Coefficient of Viscosity Force is the rate of change of momentum. We said earlier that the frictional force resisting the relative motion of the two adjacent plates was: dx u d A F η = Therefore, per unit area, equating these two equations we get: dx u d dx u d V m u N λ = 2 2 2 ρ u V u Nm = =
5 Implications Examination of this equation reveals: The viscosity of a gas is independent of pressure. This is because although at higher pressures more molecules jump between layers λ is smaller and therefore less momentum is transferred. Because the velocity increases with the absolute temperature then the viscosity increases with the absolute temperature. This last statement may seem counter intuitive but it is a consequence of the fact that because the velocity increases with temperature, so too, therefore does the transfer of momentum.

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6 Example The viscosity of carbon dioxide at 298 K and 1 atm. is 13.8 x 10 -6 kg m -1 s -1 . What is the molecular diameter? Use the mean free path to determine the molecular diameter … A A N d V 2 2 π λ= V u Nm u 2 2 λ ρ η = =
7 1 - 2 ms 411 044 . 0 298

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## This note was uploaded on 03/17/2010 for the course CH 3530 taught by Professor Consors during the Fall '10 term at WPI.

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DThurSep04 - Thermodynamics Coldest Place on Earth 1...

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