PhysicsQuestion - density－thhzpvx的部落格

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PhysicsQuestion - density

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With the assumption that the air temperature is a uniform 0.0 圖片參考：http://session.masteringphysics.com/render?expr=%7B%5Crm+km%7D as a percentage of the density at the surface?

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Using the ideal gas equation PV = nRT where P and V are the respective pressure and volume of n moles of air at temperature T. R is the Universal Gas Constant (= 8.31 J/mo.K) Wrting n = m/M, where m is the mass of air and M is its molar mass (= 0.029 kg/mol) Hence, PV = mRT/M P = (m/V)RT/M = dRT/M where d = m/V, is the density of air i.e. d = PM/RT The variation of pressure P with altitude follows the equation: P = (Po).exp(-Mgh/RT) where Po is the pressure at surface, g is the acceleration due to gravity. [You may refer to the web-page for derivation of theis formula: http://www.math24.net/barometric-formula.html ] Therefore, d = [Po.exp(-Mgh/RT)]M/RT This equation gives the variation of air density with altitude. Density at surface, (do) = (Po)M/RT thus, d/(do) = exp(-Mgh/RT) = exp(-0.029 x 9.81 x 4000/(8.31 x 273)) d/(do) = 0.606 = 60.6%

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