Question
# 1) Geochemical Box Models Consider an element X exchanging between two geochemical reservoirs A and B. Let MA and MB be the masses of
#
1) Geochemical Box Models Consider an element X exchanging between two geochemical reservoirs A and B. Let MA and MB be the masses of X in reservoirs A and B, respectively; let TA and B be the residence times of X in reservoirs A and B, respectively. Further let MT= MA + MB be the total mass of X in the two reservoirs combined. i) (15 PTS) Derive the steady state relationship: MA MT = 1+- TB ii) (10 PTS) In the limit TA >> TB, what controls the value of MA? iii) (20 PTS) Consider a situation where additional mass M' is injected into reservoir A at time t=0 increasing the total amount of element X in the system from Mo to M1, with no further injection at later times; further assume that TA >> TB, that the total mass in the altered system is M = Mo + M', and that Mo < < M'. Give an expression for MB(t) as a function of M1, TA, TB, and t. (Hint: start with an expression of dMB/dt and later integrate to get MB(t)) What is the characteristic time for MB to approach steady state? What is the characteristic time for MA to approach steady state?
Step by Step Solution
There are 3 Steps involved in it
Step: 1
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-text-image.webp)
Get Instant Access with AI-Powered Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Step: 3
![blur-text-image](https://dsd5zvtm8ll6.cloudfront.net/includes/images/document_product_info/blur-subtext-image.webp)
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started