(a) given that the atmospheric pressure at sea level (z = 0) is po = 1atm 1.013 x 105 pa, estimate the weight of the atmosphere above you. - [2 marks] (b) assume the same atmospheric pressure at sea level as in part (6a) and that the temperature at sea level is to = 288 k. using the hydrostatic balance dp pg dz and the ideal gas law, derive for an isothermal atmosphere (i) how pressure changes with height, (ii) how density changes with height and (iii) calculate the height at which pressure changes by a factor e compared to sea-level pressure. this height is called the scale height of the atmosphere. [8 marks] (c) now, suppose instead that temperature decreases uniformly with height. that is, t(2) to - tz, 10 k km is a constant lapse rate. where r (i) what is the thickness of the entire atmosphere in this case? (ii) how do pressure and density change with height in this atmosphere? (iii) do pressure and density change more or less rapidly with height compared to the isothermal atmosphere in part (6b)?