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MCS,PHD
Argosy University/ Phoniex University/
Nov-2005 - Oct-2011
Professor
Phoniex University
Oct-2001 - Nov-2016
MATHCAD help!
The saturation concentration of dissolved oxygen in fresh-water can be calculated with the equation
ln o_sf = -139.34411 + 1.575701 x 10^5/Ta - 6.642308 x 10^7/Ta^2 + 1.243800 x 10^10/ta^3 - 8.621949 x 10^11/Ta^4
where o_sf = the saturation concentration of dissolved oxygen in freshwater at 1 atm (mg/l) and T_a = absolute temperature (K). Remember that T_a = T + 273.15, where T = temperature (degrees C). According to this equation, saturation decreases with increasing temperature. For typical natural water in temperate climates, the equation can be used to determine that oxygen concentration ranges from 14.621 mg/L at 0 degrees C to 6.413 mg/L at 40 degrees C. Given a value of oxygen concentration, this formula and the bisection method can be used to solve for temperature in degrees C.
A. If the initial guesses are set as 0 and 40 degrees Celsius, how many bisection iterations would be required to determine temperature to an absolute error of .05 degrees Celsius.
B. Develop and test a bisection program in MATHCAD 15 or Prime to determine T as a function of a given oxygen concentration to a pre-specified absolute error as in (a). Given initial guesses of 0 and 40 degrees, test your program for an absolute error = .05 degrees Celsius and the following cases: osf 8, 10, 12 mg/L. Check your results.
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