ANSWER:

The atmospheric pressure is the weight exerted by the overhead atmosphere on a unit area of surface. It can be measured with a mercury barometer, consisting of a long glass tube full of mercury inverted over a pool of mercury:

Figure 2-1 Mercury barometer

When the tube is inverted over the pool, mercury flows out of the tube, creating a vacuum in the head space, and stabilizes at an equilibrium height h over the surface of the pool. This equilibrium requires that the pressure exerted on the mercury at two points on the horizontal surface of the pool, A (inside the tube) and B (outside the tube), be equal. The pressure PA at point A is that of the mercury column overhead, while the pressure PB at point B is that of the atmosphere overhead. We obtain PA from measurement of h:

(2.1)

where RHG = 13.6 g cm-3 is the density of mercury and g = 9.8 m s-2 is the acceleration of gravity. The mean value of h measured at sea level is 76.0 cm, and the corresponding atmospheric pressure is 1.013x105 kg m-1 s-2 in SI units. The SI pressure unit is called the Pascal (Pa); 1 Pa = 1 kg m-1 s-2. Customary pressure units are the atmosphere (atm) (1 atm = 1.013x105 Pa), the bar (b) (1 b = 1x105 Pa), the millibar (mb) (1 mb = 100 Pa), and the torr (1 torr = 1 mm Hg = 134 Pa). The use of millibars is slowly giving way to the equivalent SI unit of hectoPascals (hPa). The mean atmospheric pressure at sea level is given equivalently as P = 1.013x105 Pa = 1013 hPa = 1013 mb = 1 atm = 760 torr.

2.2 MASS OF THE ATMOSPHERE

The global mean pressure at the surface of the Earth is PS = 984 hPa, slightly less than the mean sea-level pressure because of the elevation of land. We deduce the total mass of the atmosphere ma:

(2.2)

where R = 6400 km is the radius of the Earth. The total number of moles of air in the atmosphere is Na = ma/Ma = 1.8x1020 moles.

Exercise 2-1. Atmospheric CO2 concentrations have increased from 280 ppmv in preindustrial times to 365 ppmv today. What is the corresponding increase in the mass of atmospheric carbon? Assume CO2 to be well mixed in the atmosphere.

Answer. We need to relate the mixing ratio of CO2 to the corresponding mass of carbon in the atmosphere. We use the definition of the mixing ratio from equation (1.3) ,

where NC and Na are the total number of moles of carbon (as CO2) and air in the atmosphere, and mC and ma are the corresponding total atmospheric masses. The second equality reflects the assumption that the CO2 mixing ratio is uniform throughout the atmosphere, and the THIRD equality reflects the relationship N = m/M. The change DmC in the mass of carbon in the atmosphere since preindustrial times can then be related to the change DCCO2 in the mixing ratio of CO2. Again, always use SI units when doing numerical calculations (this is your last reminder!):

Explanation:

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