Test: Diffusion Through Variable Cross Sectional Area - Chemical Engineering MCQ

The diffusion of component A through a conduit with a non-uniform cross-section is significantly influenced by the radius of the conduit. As the radius changes, the flux of A is affected according to Fick's law, which relates the diffusion rate to the concentration gradient and the area through which diffusion occurs.

As water evaporates from the bottom of the metal tube, the water level drops slowly over time. This is because the water molecules diffuse into the air above, leading to a decrease in the liquid level as evaporation continues.

The steady-state equation for evaporation in the metal tube takes into account the path length Z and the concentration of vapor in the air. This relationship helps to understand how the diffusion of water vapor affects the rate of evaporation as the water level changes.

The equation that relates the flux of component A to the variables in a tapered conduit is significant because it enables calculations of diffusion rates while considering changes in cross-sectional areas. This is important in processes where the geometry of the conduit impacts the flow of diffusing substances.

The evaporation of a drop of liquid from a spherical body represents radial diffusion from a point source. The diffusion occurs outward in all directions from the surface of the sphere, following Fick's law of diffusion.

Fick's law of diffusion connects the diffusion rate to the concentration gradient and the area through which the substance is diffusing. This relationship is critical in understanding how substances move from areas of high concentration to low concentration, especially in spherical systems.

The time taken for the water level to drop can be calculated by integrating the steady-state equation with respect to the changing water level. This mathematical approach allows for a precise determination of the time required for evaporation to reach a specific level.

It is assumed that the gas phase is dilute, which allows for simplifications in the equations governing diffusion. This assumption helps in deriving practical models for understanding diffusion processes in various applications.

Component A is the primary substance that diffuses through the stagnant medium of component B. This diffusion process is influenced by the concentration gradient between A and B, illustrating the fundamental principles of mass transfer.

A larger radius of the conduit typically increases the diffusion flux of component A, as a greater surface area is available for diffusion. This relationship highlights how geometry can significantly affect mass transfer rates.

The term 'surface flux' refers to the rate at which substance A passes through the surface of the sphere. This is a crucial concept in diffusion studies, as it determines how quickly the substance can move into the surrounding medium.

During the diffusion of component A through stagnant B, it is assumed that component B remains constant and does not diffuse. This assumption simplifies the analysis of the diffusion process and allows for a clearer understanding of the behavior of component A.

Fick's laws of diffusion are the mathematical models commonly used to describe the diffusion process in the scenarios discussed. These laws provide a framework for understanding how substances move in response to concentration gradients.

The geometry of the conduit, specifically if it is tapered, impacts the rate of diffusion based on its dimensions. This is because the changing radius alters the effective area through which diffusion can occur, demonstrating the importance of conduit design in mass transfer applications.

The principle underlying the calculation of diffusion rates in the discussed scenarios is that the rates are influenced by concentration gradients and surface areas. This relationship is fundamental to understanding how substances move through different mediums.

The term 'steady state' in diffusion refers to a condition where the concentration profile does not change over time, indicating that the rate of diffusion into a system equals the rate of diffusion out of it. This concept is critical in modeling and understanding diffusion processes.

The concentration of the vapor in the air above is essential for calculating the time for the water level to drop in a metal tube. This is because the rate of evaporation and, subsequently, the drop in water level depends on how much water vapor can exist in the air.

The diffusion of nutrients to a spherical microorganism occurs radially from a surface in three dimensions, which differs from diffusion in a flat surface that typically occurs in two dimensions. This three-dimensional aspect can affect how efficiently nutrients reach the microorganism.