Question

[2] The mean heat capacity (C) between two temperatures Tre and I can be calculated from ,(T)dT T-Tref (a) Use the data for the heat capacity for propane provided in the following table to calculate mean heat capacities from 400 to 1500 K using 298.3 K as the reference temperature. Fit a polynomial of suitable degree to the heat capacity data and use the resulting polynomial to evaluate the integral. (b) Calculate the mean heat capacity of propane at 1500 K using both the Simpsons and Trapezoidal rules with the given tabular data, and compare with the value determined in part (a). (300 K is close enough to 298.3 K to use as the initial value for the integration range) Temperature K Heat Capacity kJ/kgmol-K 94.01 500 50 34.06 100 41.30 150 48.79 200 56.07 273 68.74 298 73.60 300 73.93 400 112.59 600 128.70 700 142.67 800 154.77 900 163.35 1000 174.60 1100 182.67 1200 189.74 1300 195.85 1400 201.21 1500 205.89 Thermodynamics Research Center API44 Hydrocarbon Project, Selected Values of Properties of Hydrocarbon and Related Compounds, Texas A&M University, College Station, TX, 1978.

Answer 1

250 y -6E-05x2 0.2175x 17.784 R2 0.9984 200 150 100 50 0 1000 1400 0 200 400 600 800 1200 1600

A B C D E Heat Capacity (kl/kgmol-K) Temperature (K) Trapezoidal Simpson MEAN 50 34.06 100 41.3 150 48.79 200 56.07 273 68.74 73.6 298 300 73.93 94.01 400 86.1795 500 112.59 94.6329 600 128.07 102.686 700 142.67 110.34 800 154.77 117.593 124.446 900 163.35 130.9 1000 174.6 1100 182.67 136.953 1200 189.74 142.607 1300 195.85 147.86 201.21 152.713 1400 157.167 139.91 1500 205.89 155.537
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