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Engr/Math/Physics 25. Prob 5.47, 5.57 Tutorial. Bruce Mayer, PE Registered Electrical & Mechanical Engineer BMayer@ChabotCollege.edu. Problem 5.47 Chemical Rcn Order. 1 st Order Rate Eqn is Expontnential. By SemiLog Linearization we can “Discover” parameters [m & b] [C(0) & −k]
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Engr/Math/Physics 25 Prob 5.47, 5.57Tutorial Bruce Mayer, PE Registered Electrical & Mechanical EngineerBMayer@ChabotCollege.edu
Problem 5.47 Chemical Rcn Order • 1st Order Rate Eqn is Expontnential • By SemiLog Linearization we can “Discover” parameters [m & b] [C(0) & −k] • 2nd Order Eqn can be LINEARIZED as • Thus ANOTHERLinearizable Fcn
Prob Solve 1st Step → PLOT it • Advice for Every Engineer and Applied Mathematician or Physicist: • Rule-1: When in Doubt PLOT IT! • Rule-2: If you don’t KNOW when to DOUBT, then PLOT EVERYTHING
Prob 5.47 • When in Doubt PLOT (use SubPlot) • Some CURVATURE • Straight • Better Model • t X • 1/C Y
Now that the plot has identified the Rcn as 2nd Order, Make Linear Xform The 2nd Order Eqn Linear Xform of 2nd Order Reaction • Use polyfit of order-1 to generate fitting parameters contained in vector k_1overC0 • That is: k_1overC0 = [m, B2]; or • k_1overC0(1)= m = k • k_1overC0(2)= B2 = 1/C(0)
P 5.47 Answer • k_1overC0 = [m B2] = [k 1/C0] = [5.4445e-001 9.9605e+001] • k = 5.4445e-001 • k = 0.54445 • C0 =1/9.9605e+001 • 1.0040e-002 • C(0) = 0.01004
P5.57 Geometry • E-Field Governing Equation
The Distance Calcs • Using Pythagorean Theorem
meshc Plot by Loop Note that plot is TURNED
surf Plot by Loop Note that plot is TURNED