Problem 2.10 Show that the density of water vapour at saturation is given as a function of temperature by T1T A e-T//T P

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Problem 2 10 Show That The Density Of Water Vapour At Saturation Is Given As A Function Of Temperature By T1t A E T T P 1 (104.28 KiB) Viewed 62 times

Problem 2.10 Show that the density of water vapour at saturation is given as a function of temperature by T1T A e-T//T Pys = T where Ti L/Ry and A is a constant. Assuming a constant lapse rate, as in Problem 2.3, show that the following approximations are valid for heights z « To/T: = Tz Tz 11*77" (1+3) >F'exp ) T- ~ To To To Hence show that Pvs decays exponentially with z under these approximations. Evaluate the e-folding height (in km) for this decay in a tropical atmosphere with To = 300 K and г = 6.5 K km-1 and comment on how it compares with a typical pressure scale height. Check the self-consistency of your approximations in this case.