Extending the life of an aluminum smelter pot. An

QUESTION:

Extending the life of an aluminum smelter pot. An investigation of the properties of bricks used to line aluminum smelter pots was published in The American Ceramic Society Bulletin (Feb. 2005). Six different commercial bricks were evaluated. The life span of a smelter pot depends on the porosity of the brick lining (the less porosity, the longer is the life); consequently, the researchers measured the apparent porosity of each brick specimen, as well as the mean pore diameter of each brick. The data are given in the next table and saved in the SMELTPOT file.

\(\begin{array}{ccc}
\hline \text { Brick } & \begin{array}{c}
\text { Apparent } \\
\text { Porosity (\%) }
\end{array} & \begin{array}{c}
\text { Mean Pore Diameter } \\
\text { (micrometers) }
\end{array} \\
\hline \text { A } & 18.8 & 12.0 \\
\text { B } & 18.3 & 9.7 \\
\text { C } & 16.3 & 7.3 \\
\text { D } & 6.9 & 5.3 \\
\text { E } & 17.1 & 10.9 \\
\text { F } & 20.4 & 16.8 \\
\hline
\end{array}\)

Source: Based on Bonadia, P., et al. "Aluminosilicate refractories for aluminum cell linings," The American Ceramic Society Bulletin, Vol. 84, No. 2, Feb. 2005, pp. 26-31 (Table II)

a. Find the least squares line relating porosity ( y ) to mean pore diameter ( x ).

b. Interpret the y -intercept of the line.

c. Interpret the slope of the line.

d. Predict the apparent percentage of porosity for a brick with a mean pore diameter of 10 micrometers.