As part of a design calculation, you must evaluate an enthalpy change for an obscure

Chapter 8, Problem 8.42

(choose chapter or problem)

As part of a design calculation, you must evaluate an enthalpy change for an obscure organic vapor that is to be cooled from 1800C to 150C in a heat exchanger. You search through all the standard references for tabulated enthalpy or heat capacity data for the vapor but have no luck at all, until you finally stumble on an article in the May 1922 Antarctican Journal of Obscure Organic Vapors that contains a plot of Cp[cal/(gC)] on a logarithmic scale versus [T(C)]1=2 on a linear scale. The plot is a straight line through the points (Cp 0:329, T1=2 7:1) and (Cp 0:533, T1=2 17:3). (a) Derive an equation for Cp as a function of T. (b) Suppose the relationship of Part (a) turns out to be Cp 0:235 exp0:0473T1=2 and that you wish to evaluate H^cal/g Z 150C 1800C Cp dT First perform the integration analytically, using a table of integrals if necessary; then write a spreadsheet or computer program to do it using Simpsons rule (Appendix A.3). Have the program evaluate Cp at 11 equally spaced points from 150C to 1800C, estimate and print the value of H, and repeat the calculation using 101 points. What can you conclude about the accuracy of the numerical calculation?