02-Snow-Atmosphere

02-Snow-Atmosphere - Dependence of pressure on height ESM...

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3/24/2008 1 ESM 236: ESM 236: Snow crystals in Snow crystals in atmosphere and snowpack Spring 2008 1 Bare minimum about the gas laws • Ideal gas law PV=NkT P pressure, V volume, N number of molecules, k Boltzmann’s constant (1.38 × 10 –23 J K –1 ), T absolute temperature ( ° K) • Because N is big and k is small, we often use 2 Spring 2008 PV=N m R T instead N m number of moles (1 mole has 6.022 × 10 23 molecules—Avogadro’s number N a ) R =N a k= 8.314 J mol –1 K –1 , the universal gas constant • Equation of state P= ρ R * T/M density (kg m –3 ), M molecular weight (kg mol –1 ) Gas laws, applied to the atmosphere • Dalton’s law P=P 1 +P 2 +P 3 …= R * T/ M , where M is the average molecular weight • The atmosphere is dry air ( M d =0.02894 kg 3 Spring 2008 mol –1 ) and water vapor ( M w =0.018 kg mol –1 ) –So P=P d +e (pressure of the dry air + vapor pressure) e= w R * T/M w , where w is the water vapor density, or absolute humidity Dependence of pressure on height • The hydrostatic equation * * a a PM dP gg dz RT gM dP dz =− 6 8 10 km Spring 2008 0 * 0 0 * 0 * 0 1 exp ( at 0) exp ( average) P exp ( 8 km) P z a a a P R T gM P dz P P z PT R gM z P T P z h hg M ⎛⎞ = = ⎜⎟ ⎝⎠ ≈− = ≈− = 0 2 4 0 200 400 600 800 1000 Height, k Pressure, mb Evaporation and condensation of water • Water vapor is the only gas in Earth’s atmosphere that can condense (and freeze) at ordinary water vapor Vapor pressure e 5 Spring 2008 at ordinary temperatures Equilibrium vapor pressure (or saturation vapor pressure) depends on temperature only water Saturation vapor pressure 25 30 35 40 45 pressure, mb
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This note was uploaded on 08/06/2008 for the course ESM 236 taught by Professor Dozier during the Spring '08 term at UCSB.

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02-Snow-Atmosphere - Dependence of pressure on height ESM...

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