Wednesday, July 25, 2012

Equilibrium Changes

  The equilibrium condition, αA = λB, allows us to derive a formula for the changes in B. The production rate, α, is dependent on the flux of cosmic rays, A is the quantity of nitrogen, λ is the removal rate for C-14 associated with carbon sinks and B is the equilibrium quantity of C-14. Taking partial derivatives of the equation allows us to determine the partial derivatives of B which can be inserted into the derivative chain rule. The resulting equation only involves relative changes. Note that increases in α produce increases in B while increases in λ result in decreases in B which may help in identifying the source of the fluctuations in B. However the observation of an increase in the C-14 concentration in Summer might be due to more than one cause such as an increase in the number of protons from the solar wind due to the tilt of the magnetic pole towards the Sun in summer or a decrease in the solubility of CO2 in the oceans with increasing temperature.
  Supplemental (26 Jul): Solubility of CO2. A similar equilibrium condition (11-5) applies.

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