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Chapter 14: Problem 71

Express the mass flow rate of water vapor through a wall of thickness \(L\) in terms of the partial pressure of water vapor on both sides of the wall and the permeability of the wall to the water vapor.

Short Answer

Expert verified
Answer: The formula to express the mass flow rate of water vapor through a wall of thickness L is m = -(k * A * ΔP) / L, where m is the mass flow rate, k is the permeability of the wall, A is the area of the wall, and ΔP is the difference in partial pressure between the two sides of the wall.

Step by step solution

01

Write down the Fick's law of diffusion formula

The formula for Fick's law of diffusion is: J = -k * (ΔP / L) Where: J is the diffusion flux k is the permeability of the wall ΔP is the difference in partial pressure between the two sides of the wall L is the thickness of the wall
02

Calculate the mass flow rate

To find the mass flow rate of water vapor (m), we need to multiply the diffusion flux (J) by the area of the wall (A). This gives us: m = J * A
03

Substitute Fick's law formula into the mass flow rate formula

Now let's substitute the Fick's law formula (from Step 1) into the mass flow rate formula (from Step 2): m = (-k * (ΔP / L)) * A
04

Rearrange the formula to express the mass flow rate in terms of the partial pressure and permeability

We can now rearrange the formula to better express the mass flow rate (m) in terms of the partial pressure difference (ΔP) and permeability (k): m = -(k * A * ΔP) / L This formula represents the mass flow rate of water vapor through a wall of thickness L, in terms of the partial pressure of water vapor on both sides of the wall and the permeability of the wall to the water vapor.

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Most popular questions from this chapter

Consider a shallow body of water. Is it possible for this water to freeze during a cold and dry night even when the ambient air and surrounding surface temperatures never drop to \(0^{\circ} \mathrm{C}\) ? Explain.

Consider a thin layer of liquid water on a concrete surface. The surrounding air is dry with a convection heat transfer coefficient of \(50 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The liquid water has an emissivity of \(0.95\), and the air and surrounding temperature is \(30^{\circ} \mathrm{C}\). If the layer of liquid water has a uniform temperature of \(20^{\circ} \mathrm{C}\), determine the conduction heat flux through the concrete.

Does a mass transfer process have to involve heat transfer? Describe a process that involves both heat and mass transfer.

Explain how vapor pressure of the ambient air is determined when the temperature, total pressure, and relative humidity of the air are given.

In transient mass diffusion analysis, can we treat the diffusion of a solid into another solid of finite thickness (such as the diffusion of carbon into an ordinary steel component) as a diffusion process in a semi-infinite medium? Explain.
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