A spherical mothball initially with radius, Ro, is shrinking in volume due to the sublimation of naphthalene through the air in a large room. At room temperature (T) and pressure (PT), the naphthalene (with molecular weight as MWa) in the mothball exerts a vapor pressure (VPa). It is of interest to investigate the rate at which the mothball is shrinking due to the diffusion of naphthalene in an air-rich environment.
A spherical mothball initially with radius, Ro, is shrinking in volume due to the sublimation of naphthalene through the air in a large room. At room temperature (T) and pressure (PT), the naphthalene (with molecular weight as MWa) in the mothball exerts a vapor pressure (VPa). It is of interest to investigate the rate at which the mothball is shrinking due to the diffusion of naphthalene in an air-rich environment.
A. Illustrate the physical model/s that can describe the diffusion of naphthalene through the air-rich environment (room). Indicate the control volume/s (differential volume/s) as an expression of the transfer area and distance. Specify the components needed in establishing the shell balance. Indicate the boundary conditions and illustrate the direction of transfer in each physical model. Note: Express the radial distance from the mothball surface as r, while the shrinking radius of the mothball is expressed as R. Use and define subscripts, as necessary.
B. For each physical model, specify the unsteady state mole balance based on the components illustrated in A.
C. Derive the steady state differential shell balance equations for the bulk gas phase, and on the surface of the mothball. How may the two differential equations be related?
D. Derive the concentration profile (in terms of partial pressure) of naphthalene (component A) in air as a function of the radial distance from the mothball surface. What are the pertinent boundary conditions that can be stated to derive this model?
E. Derive the equation to compute for the time at which the mothball is shrinking [t = f(R)]. What are the pertinent boundary conditions that can be used to solve this?
Step by step
Solved in 5 steps with 9 images
