Band Models — Lesson 8

This lesson covers the concept of band absorptance in gases, focusing on its definition, calculation, and relevance in engineering. It explains how band absorptance is a function of the partial pressure of the absorbing gas, the length scale, line section parameter, and the gas temperature. The lesson also discusses the difference between absorptivity and emissivity, and how these properties are influenced by factors such as path length, line structure parameter, and temperature. It further explores the Elsasser band model and the correlated k method for calculating absorptivity and emissivity.

Video Highlights

02:32 - Explanation of how to evaluate emissivity in absorbed gas based on the absorption.
13:14 - Explanation of the Elsasser band model, which considers a large number of identical lines in the spectral
25:35 - Discussion on the empirical expressions for absorptance based on laboratory measurements
32:44 - Explanation of how to use the concept of band absorptance in real examples, with a focus on radiative equilibrium.
48:05 - Discussion on the challenges in calculating absorption coefficient of gases due to large fluctuations in absorption coefficient.
54:59 - Introduction to the correlated k method, which simplifies the computation of absorptivity and emissivity by re-mapping the absorption coefficient.

Key Takeaways

- Band absorptance is integral over the band of the absorptivity within the band.
- The band absorptance is a function of the partial pressure of the absorbing gas, the length scale, line section parameter, and the gas temperature.
- Emissivity and absorptivity are weighted differently, with emissivity being a function of path length, beta i, and temperature, while absorptivity is a function of path length, line structure parameter, gas temperature, and the source temperature.
- The Elsasser band model is a simplified model that assumes a series of lines of identical height and spacing.
- The correlated k method is a more efficient way to compute absorptivity and emissivity compared to the line-by-line method.