Solved: The article “Low-Temperature Heat Capacity and

Chapter 8, Problem 18SE

(choose chapter or problem)

The article “Low-Temperature Heat Capacity and Thermodynamic Properties of 1,1,1-trifluoro-2, 2-dichloroethane” (R. Varushchenko and A. Druzhinina, Fluid Phase Equilibria, 2002:109–119) presents measurements of the molar heat capacity \((y)\) of 1,1,1-trifluoro-2,2-dichloroethane (in \(\mathrm {J \cdot K^{-1} \cdot mol^{-1}}\)) at several temperatures \((x)\) in units of 10 K. The results for every tenth measurement are presented in the following table.

a. Fit the simple linear model \(y=\beta_{0}+\beta_{1} x+\varepsilon\). Make a residual plot, and comment on the appropriateness of the model.

b. Fit the simple linear model \(y=\beta_{0}+\beta_{1} \ln x+\varepsilon\). Make a residual plot, and comment on the appropriateness of the model.

c. Compute the coefficients and their standard deviations for polynomials of degrees 2, 3, 4, and 5. Make residual plots for each.

d. The article cited at the beginning of this exercise recommends the quartic model \(y=\beta_{0}+\beta_{1} x+\beta_{2} x^{2}+\beta_{3} x^{3}+\beta_{4} x^{4}+\varepsilon\). Does this seem reasonable? Why or why not?

Equation Transcription:

Text Transcription:

(y)

J{cdot}K^{-1}{cdot}mol^-1

(x)

y=beta_0+beta_1x+varepsilon

y=beta_0+beta_1 ln x+varepsilon

y=beta_0+beta_1x+beta_2x^2+beta_3x^3+beta_4x^4+varepsilon