A large deep lake, which initially had a uniform oxygen concentration, has its surface concentration suddenly raised and maintained at a higher concentration level. Assuming the lake water to be static, reduce the general differential equation for mass transfer to write the specific differential equation using the diffusivity of O2 (A) through water (B), DAB, for:
a) the transfer of oxygen into the lake without the presence of a chemical reaction. State all assumptions.
b) the transfer of oxygen into the lake that occurs with the simultaneous disappearance of oxygen by a first-order biological reaction with a rate constant k (> 0).