As part of a design calculation, you must evaluate an enthalpy change for an obscure organic vapor that is to be cooled from 1800°C to 150°C 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 Vapor5 that Contains a plot of Cp [cal / (g ∙ °C)] 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 C, as a function of T.

(b) Suppose the relationship of part (a) turns out to be and that you wish to evaluate first perform the integration analytically, using a table of integrals if necessary; then write a spreadsheet or computer program to do it using Simpson’s rule (Appendix A.3). Have the program evaluate Cp at 11 equally spaced points from 150°C to 1800°C, estimate and print the value of ΔH, and repeat the calculation using 101 points. What can you conclude about the accuracy of the numerical calculation?