Question

What is diffusion velocity? How does it affect the mass-average velocity? Can the velocity of a species in a moving medium relative to a fixed reference point be zero in a moving medium? Explain.

Short answer

Explain. Answer: Yes, the velocity of a species in a moving medium can be zero relative to a fixed reference point if the species has a velocity in the opposite direction of the mass-average velocity with the same magnitude. This counteracts the mass-average velocity and results in a net velocity of zero relative to the fixed reference point.

Step-by-step solution

Defining Diffusion Velocity

Diffusion velocity is the velocity at which a substance (such as a gas or a solute) moves due to its concentration gradient. In other words, it is the rate at which a substance moves from a region of higher concentration to a region of lower concentration. The driving force behind diffusion is the difference in concentration between the two regions; this difference leads to a net movement of the substance until an equilibrium is reached.

Relation between Diffusion Velocity and Mass-Average Velocity

Mass-average velocity is a weighted average of the velocities of individual species in a mixture, with each velocity weighted by the mass fraction of the corresponding species. It is calculated as follows: Mass-average velocity = Sum(mass fraction of species × velocity of species) When considering diffusion, the mass-average velocity affects the diffusion velocity of a substance within the mixture. If the mass-average velocity is high, the diffusion velocity of the substance will also be high since the substance will be moving in response to both the mass-average velocity and its own concentration gradient.

Velocity of a Species Relative to a Fixed Reference Point

The velocity of a species in a moving medium can be zero relative to a fixed reference point under certain conditions. First, the species must be in a medium that is moving relative to the reference point. Second, the species must have a velocity in the opposite direction of the mass-average velocity with the same magnitude. For instance, let's assume a gas mixture is moving with a mass-average velocity of 5 m/s to the right relative to a reference point. The velocity of a species (e.g., a gas molecule) within the medium would have to be -5 m/s (5 m/s to the left) relative to the medium to have a net velocity of zero relative to the fixed reference point. In conclusion, it is possible for the velocity of a species in a moving medium to be zero relative to a fixed reference point. This occurs when the species has a velocity in the opposite direction of the mass-average velocity with the same magnitude.