Question

The presence of CO2 in solution is essential to the growth of aquatic plant life, with CO2 used as a reactant in the photosynthesis. Consider a stagnant body of water in which the concentration of CO2 (rho_A) is everywhere zero. At time t = 0, the water is exposed to a source of CO2, which maintains the surface (x = 0) concentration at a fixed value rho_(A,0). For time t = 0, CO2 will begin to accumulate in the water, but the accumulation is inhibited by CO2 consumption due to photosynthesis. The time rate at which this consumption occurs per unit volume is equal to the product of a reaction rate constant k1 and the local CO2 concentration rho_A (x,t).
a. Write a differential equation that could be used to determine the variation in CO2 concentration with both depth and time. List any assumptions used. What does each term in the equation represent physically?

b. Write appropriate boundary conditions that could be used to obtain a particular solution, assuming a "deep" body of water. What would be the form of this equation for negligible CO2 consumption (i.e.k1 0)?

Answer 1

Answer:

The differential equations and the boundary conditions(initial and final)are shown in the attachment