dolution

Using glass to encapsulate waste. Since glass is not subject to radiation damage, encapsulation of waste in glass is considered to be one of the most promising solutions to the problem of lowlevel nuclear waste in the environment. However, glass undergoes chemical changes when exposed to extreme environmental conditions, and certain of its constituents can leach into the surroundings. In addition, these chemical reactions may weaken the glass. These concerns led to a study undertaken jointly by the Department of Materials Science and Engineering at the University of Florida and the U.S. Department of Energy to assess the utility of glass as a waste encapsulant material.† Corrosive chemical solutions (called corrosion baths) were prepared and applied directly to glass samples containing one of three types of waste (TDS3A, FE, and AL); the chemical reactions were observed over time. A few of the key variables measured were y = Amount of silicon (in parts per million) found in solution at end of experiment. (This is both a measure of the degree of reakdown in the glass and a proxy for the amount of radioactive species released) into the environment. x1 = Temperature (◦C) of the corrosion bath x2 = ⎧ ⎪⎨ ⎪⎩ 1 if waste type TDS-3A 0 if not x3 = ⎧ ⎪⎨ ⎪⎩ 1 if waste type FE 0 if not Waste type AL is the base level. Suppose we want to model amount y of silicon as a function of temperature (x1) and type of waste (x2, x3).

(a) Write a model that proposes parallel straightline relationships between amount of silicon and temperature, one line for each of the three waste types.

(b) Add terms for the interaction between temperature and waste type to the model of part a.

(c) Refer to the model of part b. For each waste type, give the slope of the line relating amount of silicon to temperature.

(d) Explain how you could test for the presence of temperature–waste type interaction.