The controlled release of pheromones can be used to attract flying crop-damaging insects to a trap as a safer alternative to pesticides. A simple pheromone release device is shown in the figure below (not to scale). The pheromone is a waxy solid cylinder, which sublimes and is transported away into the flowing air. The sublimation pressure of the pheromone at 27°C is 0.50 mmHg, its molecular mass is 200, and its diffusion volume is  = 80 cm³/mol. The air temperature is 27°C. The device will be placed in a location where the wind speed is a constant 2.0 m/s. The density of the solid pheromone is 1,200 kg/m³, the initial diameter of the pheromone cylinder is 0.02 m, and its length is 0.4 m.

(a) Estimate as accurately as possible the diffusion coefficient of the pheromone in air at 27°C and 1 atm.

(b) Calculate the initial value of the mass transfer coefficient for pheromone transport into the air.

(c) Calculate the initial rate of pheromone release. (d)

Derive an explicit equation to predict how the radius of the cylinder will change as a function of time. Note that the mass transfer coefficient will vary with the cylinder radius.

(e) Integrate your equation in part

(d) and determine the time required for the cylinder radius to decrease to one half of the initial value.

FIGURE P.13.7.: