= 3. The atmosphere of Jupiter has many different cloud layers, including NH3 and water vapor. Almost all of the mass at these altitudes is in H2 and He gas. a. Starting at the altitude of the NH3 cloud tops where the local temperature is 140K, a very long vertical column of 1m area and height extending upwards into space is found to contain a total of 5x1029 molecules of H2 and 1029 molecules of He. Find an expression for the pressure at the cloud tops (Pc) and using this information give a numerical value for the pressure. b. Below the NH3 cloud tops the atmosphere heat distribution is dominated by convection. The temperature increases with depth (s) at a constant adiabatic lapse rate of dT/ds = 2x10-3 K m-?. Write down an expression for the temperature T(s) below the cloud tops and then the equation of hydrostatic equilibrium including explicitly the variation in temperature with depth. c. Integrate the equation of hydrostatic equilibrium including explicitly the variation in temperature with depth found in part b) to derive an expression for the pressure as a function of depth, P(s). Use the known values of pressure and temperature at the NH3 cloud tops to evaluate any constants. Assume the mean molecular weight of the atmosphere below the cloud tops is the same as the atmosphere above the cloud tops. d. Water ice clouds form at a depth below the NH3 cloud tops where the temperature reaches 280 K. Find the depth, Swater, of this level below the level of Pc and the associated pressure, P water