Exchange Between Reservoirs

The exchange of carbon between atmosphere and surface ocean is characterized by a transfer time distime 

The first term on the right is the exchange of water, and the second term is the effect of the settling particles. The contribution of particulate phosphate is negligibly small. 

The total dissolved carbon and alkalinity in the deep sea are given by 

In this system, the sum of carbon in all reservoirs and the sum of alkalinity in all reservoirs both remain constant. I am not yet considering possible sources or sinks of carbon and alkalinity. 

The starting values and parameters are the following (Broecker and Peng, 1982, p. 69)  

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Within this large-scale approach to the formation of the MBWB ocean unit, the dependences of the fluxes of water in its different phases on environmental parameters remain uncertain. Apparently, the mass exchange between reservoirs, v and l can be described by the simplest linear scheme ws = Wosaos — WOLaOL /Tsi, where Td is the time it takes to equalize levels Wos and WOL, and aos and aOL are the areas of... 

Metabolic Functions. Bones act as a reservoir of certain ions, in particular Ca " and which readily exchange between bones and blood. 

The second item means that heat exchange between system and surroundings must occur at the temperature of the surroundings, presumed to constitute a heat reservoir at a constant and uniform temperature... 

Figure 2. (A.) The radionuclides in an aquifer are divided into three reservoirs groundwater, the host aquifer minerals, and adsorbed onto active surfaces. Also shown are the processes adding to a daughter nuclide (closed circles) in the groundwater of weathering, advection, recoil from decay of parent atoms ( P ) in the aquifer minerals, and production by parent decay, the processes of losses of a radionuclide of advection and decay, and exchange between dissolved and adsorbed atoms.

The fossil C02 brought into the atmosphere does not contain 14C and leads to a 14C dilution. Without exchanges between the atmosphere and the other reservoirs, a fossil C02 input of 10 percent until 1950 would have led to a decrease of the 14C/C ratio by 10 percent. The actually observed reduction of the 14C/C ratio, however, is of the order of 2 percent, i.e., much smaller. This is to be explained by the exchange with the biospheric and oceanic reservoirs. Again a dilution factor D14p <. of the system can be calculated. ... 

Equation 1.2 assumes that the concentration of C is constant throughout the ocean, i.e., that the rate of water mixing is much fester than the combined effects of any reaction rates. For chemicals that exhibit this behavior, the ocean can be treated as one well-mixed reservoir. This is generally only true for the six most abundant (major) ions in seawater. For the rest of the chemicals, the open ocean is better modeled as a two-reservoir system (surface and deep water) in which the rate of water exchange between these two boxes is explicitly accoimted for. 

There are different time scales associated with the various emissions and uptake processes. Two terms that are frequently used are turnover time and response or adjustment) time. The turnover time is defined as the ratio of the mass of the gas in the atmosphere to its total rate of removal from the atmosphere. The response or adjustment time, on the other hand, is the decay time for a compound emitted into the atmosphere as an instantaneous pulse. If the removal can be described as a first-order process, i.e., the rate of removal is proportional to the concentration and the constant of proportionality remains the same, the turnover and the response times are approximately equal. However, this is not the case if the parameter relating the removal rate and the concentration is not constant. They are also not equal if the gas exchanges between several different reservoirs, as is the case for C02. For example, the turnover time for C02 in the atmosphere is about 4 years because of the rapid uptake by the oceans and terrestrial biosphere, but the response time is about 100 years because of the time it takes for C02 in the ocean surface layer to be taken up into the deep ocean. A pulse of C02 emitted into the atmosphere is expected to decay more rapidly over the first decade or so and then more gradually over the next century. 

Bones act as a reservoir of certain ions, in particular Ca and PO/1". which readily exchange between bones and blood. Bone structure comprises a strong organic matrix combined with an inorganic phase which is principally hydroxyapatite, 3 CadPO/l- CaiOHH. Bones contain two forms of hydroxyapatite. The less soluble crystalline form contributes to the rigidity of the structure. The crystals are quite stable, hut because of the small size present a very large surface area available lor rapid... 

An important stage in understanding the processes of C02 exchange between biospheric reservoirs is study of the laws of the development of various ecosystems in pre-industrial epochs, when there was little human involvement. Natural carbon fluxes between the atmosphere, oceans, land ecosystems, and inland water bodies... 

Due to the irreversible heat exchange between the four heat reservoirs (for T0 = 300 K and T, = 600 K), the real maximum power is found to be close to a value of 0.3 rather than the ideal value of 0.5. The maximum power is found at an optimal flow rate (32 corresponding to an optimal set of temperatures T2 and T3/ satisfying the Carnot relation... 

The free 14C atoms formed in the atmosphere become oxidized and form 14C02 which is rapidly mixed throughout the atmosphere (Libby, 1952). This 14C then becomes incorporated into other reservoirs such as the biosphere, as plants fix carbon during the process of photosynthesis the exchange between the atmosphere and the surface ocean is estimated to take approximately 5 y (Broecker and Peng, 1982). 

One can also partition the external CT energy of electron exchange between any given molecular system M and the reservoir r. Let... 

It is also instructive to determine the entropy change involved in a compound system consisting of two large reservoirs maintained at temperatures Th and Tc (< Th), respectively. Let an amount of heat Q be exchanged between them. The increase in entropy of the compound system now is Q[l/Tc - 1/Th] > 0 so long as the temperature in each reservoir remains almost unaffected by this heat exchange. 

In order that the heat exchanges between the gas and the reservoirs take place reversibly it is essential that the temperature of the gas is made equal to that of the particular reservoir before they are brought into thermal contact. This change in temperature must be effected reversibly and without recourse to any other heat reservoir. Such a change can be effected by adiabatic and reversible compression or expansion of the gas. 

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