Beijing University of Chemical Technology Differential Equations Summer 2017 Pro
ID: 3142768 • Letter: B
Question
Beijing University of Chemical Technology Differential Equations Summer 2017 Projeet: Xylan Hydrolysis in a Batch Reactor and Biography of a Great Mathematician ned: 315,201 Tue: 20/6/2017, ++ Please solve the following problems. Present your results in the form of a neat and organized report. Note that this project will form 10% ofyour overall numerical grade. 1. Xylan Hydrolysis in a Batch Reactor (80 points) 100 g of sugar maple wood meal are extracted with water in a batch reactor at 160°C. The sequence of reactions in the reactor can be conceptualized by the following scheme: ki k2 XylanXylooligonwrs (wood) Xylose- (liquor) (liquor) where k. (-1.67 h and ks(= 0.34 h'') are first-order reaction rate constants. The mass conservation equations describing the temporal variation of the amounts of xylan (M xylooligomers (Maig) and xylose (M), all expressed in g, in the reactorare given by dM dr dM dr dM dr wheret is the reaction time, a is the susceptible fraction of xylan in sugar maple 0.83) and My is the initial amount of xylan in the raw wood (= 15 g). There are no xylooligomers or xylose present initially in the liquor. Derive analytical expressions for Mayta(C), Moigt) and Mahosel) and, using the data given, plot them as functions of t for t varying from 0 to 10 h.From your solution, derive expressions for the maximum amount of xylooligomers in the reactor and the time when this maximum occurs, and calculate them using the data supplied. What are the ultimate amounts of xylan, xylooligomers and xylose in the reactor. 2. Biography of a Great Mathematician Write a brief biography (1-2 pages) of a great mathematician of your choice. (20 points)Explanation / Answer
2) brief biography of great mathematician Archimedes
Archimedes is a mathematician famous for the Archimedes Principle, and many other important contributions to the world of mathematics and physics.
He is one of the most famous people in the field of mathematics and physics. He applied mathemetics to physical elements and how they work, and this is why he has earned his place as one of the greatest mathematicians of all time. His works and some of his most important contributions in the world of mathematics, includes his most famous contribution of all, the Archimedes' Principle
Archimedes' Principle :
Principle states that any kind of body which is immersed in any kind of fluid is subjected to an exerted upward force that is equal to the weight that is displaced by the body. This upward force is called “buoyancy". The formulation of this principle is said to have come from a personal experience of Archimedes where he observed that he displaced water when he stepped into a bath. This legend also involves him rushing out from the bath and out into the streets while yelling “Eureka!" which is the Greek word for the phrase “I have found it!"
Early Life :
Archimedes was born in Syracuse, Sicily around the year 287 BC. Little is known about his family, only that his father was named Phidias. It is thought that his father, an astronomer, was related to the king of Syracuse at that time, Hieron II. There is no clear indication of this information about his education, but there documents that support that he had many friends in Alexandria and he sent the results of his studies in mathematics to Alexandria with highly personal notes.
Works :
His study of mathematics and the application of these studies led him to invent compound pulley systems, the planetarium and several war machines that were used in defending Syracuse from enemies. It is also possible that he was involved in the invention of the water organ and the water screw.
He did not just study existing literature involving mathematics, but he also initiated and pioneered a number of fields of science such as hydrostatics, pycnometry and static mechanics. He also did a lot for integral calculus and mathematical physics, so much so that he is called “the father of integral calculus" and “the father of mathematical physics".
His findings, theories and results of his studies are forever preserved in his published works that include The Sandreckoner, On Spirals, On Conoids and Spheroids, Quadrature of the Parabola, On Plane Equilibriums, On Floating Bodies and Measurement of a Circle.
End of His Life :
Archimedes died in 212 BC when he was killed by a soldier from the Roman army, which was invading Syracuse at the time. The soldier did not know who he was, and unknowingly ended the life of one of the most brilliant minds the Roman empire could have used for its own benefit.
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