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In a diving-chamber experiment, a human subject breathed a mixture of \( \text{O}_2 \) and He while small areas of his skin were exposed to nitrogen gas. After some time, the exposed areas became blotchy, with small blisters forming on the skin. Model the skin as consisting of two adjacent layers, one of thickness \( \delta_1 \) and the other of thickness \( \delta_2 \). If counterdiffusion of He out through the skin occurs at the same time as \( \text{N}_2 \) diffuses into the skin, at what point in the skin layers is the sum of the partial pressures a maximum? If the saturation partial pressure for the sum of the gases is 101 kPa, can the blisters be a result of the sum of the gas partial pressures exceeding the saturation partial pressure and the gas coming out of the solution (i.e., the skin)? Before answering any of these questions, derive the concentration profiles for \( \text{N}_2 \) and He in the skin layers. **Diffusivity of He and \( \text{N}_2 \) in the inner skin layer:** - He: \( 5 \times 10^{-7} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 1.5 \times 10^{-7} \, \text{cm}^2/\text{s} \) **Diffusivity of He and \( \text{N}_2 \) in the outer skin layer:** - He: \( 10^{-5} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 3.3 \times 10^{-4} \, \text{cm}^2/\text{s} \) --- ### Table: Skin Boundary Partial Pressures and Thickness | | External Skin Boundary Partial Pressure | Internal Skin Boundary Partial Pressure | |----------------------|----------------------------------------|----------------------------------------| | \( \text{N}_2 \) | 101 kPa | 0 | | He | 0 | 81 kPa | | Thickness \( \delta_1 \) | 20 μm (Stratum corneum) | | | Thickness \( \delta_2 \) | 80 μ

In a diving-chamber experiment, a human subject breathed a mixture of \( \text{O}_2 \) and He while small areas of his skin were exposed to nitrogen gas. After some time, the exposed areas became blotchy, with small blisters forming on the skin. Model the skin as consisting of two adjacent layers, one of thickness \( \delta_1 \) and the other of thickness \( \delta_2 \). If counterdiffusion of He out through the skin occurs at the same time as \( \text{N}_2 \) diffuses into the skin, at what point in the skin layers is the sum of the partial pressures a maximum? If the saturation partial pressure for the sum of the gases is 101 kPa, can the blisters be a result of the sum of the gas partial pressures exceeding the saturation partial pressure and the gas coming out of the solution (i.e., the skin)? Before answering any of these questions, derive the concentration profiles for \( \text{N}_2 \) and He in the skin layers. **Diffusivity of He and \( \text{N}_2 \) in the inner skin layer:** - He: \( 5 \times 10^{-7} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 1.5 \times 10^{-7} \, \text{cm}^2/\text{s} \) **Diffusivity of He and \( \text{N}_2 \) in the outer skin layer:** - He: \( 10^{-5} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 3.3 \times 10^{-4} \, \text{cm}^2/\text{s} \) --- ### Table: Skin Boundary Partial Pressures and Thickness | | External Skin Boundary Partial Pressure | Internal Skin Boundary Partial Pressure | |----------------------|----------------------------------------|----------------------------------------| | \( \text{N}_2 \) | 101 kPa | 0 | | He | 0 | 81 kPa | | Thickness \( \delta_1 \) | 20 μm (Stratum corneum) | | | Thickness \( \delta_2 \) | 80 μ

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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In a diving-chamber experiment, a human subject breathed a mixture of \( \text{O}_2 \) and He while small areas of his skin were exposed to nitrogen gas. After some time, the exposed areas became blotchy, with small blisters forming on the skin. Model the skin as consisting of two adjacent layers, one of thickness \( \delta_1 \) and the other of thickness \( \delta_2 \). If counterdiffusion of He out through the skin occurs at the same time as \( \text{N}_2 \) diffuses into the skin, at what point in the skin layers is the sum of the partial pressures a maximum? If the saturation partial pressure for the sum of the gases is 101 kPa, can the blisters be a result of the sum of the gas partial pressures exceeding the saturation partial pressure and the gas coming out of the solution (i.e., the skin)? Before answering any of these questions, derive the concentration profiles for \( \text{N}_2 \) and He in the skin layers. **Diffusivity of He and \( \text{N}_2 \) in the inner skin layer:** - He: \( 5 \times 10^{-7} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 1.5 \times 10^{-7} \, \text{cm}^2/\text{s} \) **Diffusivity of He and \( \text{N}_2 \) in the outer skin layer:** - He: \( 10^{-5} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 3.3 \times 10^{-4} \, \text{cm}^2/\text{s} \) --- ### Table: Skin Boundary Partial Pressures and Thickness | | External Skin Boundary Partial Pressure | Internal Skin Boundary Partial Pressure | |----------------------|----------------------------------------|----------------------------------------| | \( \text{N}_2 \) | 101 kPa | 0 | | He | 0 | 81 kPa | | Thickness \( \delta_1 \) | 20 μm (Stratum corneum) | | | Thickness \( \delta_2 \) | 80 μ
Transcribed Image Text:In a diving-chamber experiment, a human subject breathed a mixture of \( \text{O}_2 \) and He while small areas of his skin were exposed to nitrogen gas. After some time, the exposed areas became blotchy, with small blisters forming on the skin. Model the skin as consisting of two adjacent layers, one of thickness \( \delta_1 \) and the other of thickness \( \delta_2 \). If counterdiffusion of He out through the skin occurs at the same time as \( \text{N}_2 \) diffuses into the skin, at what point in the skin layers is the sum of the partial pressures a maximum? If the saturation partial pressure for the sum of the gases is 101 kPa, can the blisters be a result of the sum of the gas partial pressures exceeding the saturation partial pressure and the gas coming out of the solution (i.e., the skin)? Before answering any of these questions, derive the concentration profiles for \( \text{N}_2 \) and He in the skin layers. **Diffusivity of He and \( \text{N}_2 \) in the inner skin layer:** - He: \( 5 \times 10^{-7} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 1.5 \times 10^{-7} \, \text{cm}^2/\text{s} \) **Diffusivity of He and \( \text{N}_2 \) in the outer skin layer:** - He: \( 10^{-5} \, \text{cm}^2/\text{s} \) - \( \text{N}_2 \): \( 3.3 \times 10^{-4} \, \text{cm}^2/\text{s} \) --- ### Table: Skin Boundary Partial Pressures and Thickness | | External Skin Boundary Partial Pressure | Internal Skin Boundary Partial Pressure | |----------------------|----------------------------------------|----------------------------------------| | \( \text{N}_2 \) | 101 kPa | 0 | | He | 0 | 81 kPa | | Thickness \( \delta_1 \) | 20 μm (Stratum corneum) | | | Thickness \( \delta_2 \) | 80 μ
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