In Problem 14.37, NO₂ transport by diffusion in a stagnant atmosphere was considered for steady-state conditions. However, the problem is actually time dependent, and a more realistic approach would account for transient effects. Consider the ground level emission of NO₂ to begin in the early morning (at t = 0), when the NO₂ concentration in the atmosphere is everywhere zero. Emission occurs throughout the day at a constant flux N''_A,0, and the NO₂ again experiences a first-order photochemical reaction in the atmosphere (NA = –k₁CA).

(a) For a differential element in the atmosphere, derive a differential equation that could be used to determine the molar concentration CA(x, t). State appropriate initial and boundary conditions

(b) Obtain an expression for C_A (x, t) under the special condition for which photochemical reactions may be neglected. For this condition what are the molar concentrations of NO₂ at ground level and at 100-m elevation 3 h after the start of the emissions, if N''_A,0 = 3 x 10^-11k mol/s ∙ m² and D_AB = 0.15 x 10^-4 m²/s?