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# How Do We Estimate Melt Density?

This activity was selected for the On the Cutting Edge Reviewed Teaching Collection

This activity has received positive reviews in a peer review process involving five review categories. The five categories included in the process are

• Scientific Accuracy
• Alignment of Learning Goals, Activities, and Assessments
• Pedagogic Effectiveness
• Robustness (usability and dependability of all components)
• Completeness of the ActivitySheet web page

This material was originally developed by Spreadsheets Across the Curriculum as part of its collaboration with the SERC Pedagogic Service.

#### Summary

In this Spreadsheets Across the Curriculum activity, students will use the thermodynamic properties of silicates to estimate melt density at high temperatures and pressures. Students will sum the mole fractions of several different oxides, with different densities, to calculate the total density of the melt. The molar volume and compressibility of each oxide will also be factored in the total melt density. This is a self-paced activity in which students follow a PowerPoint presentation to create spreadsheets and graphs using Excel.

## Learning Goals

Students will:
• Use chemical analyses to understand melt properties and the nature of magma movement.
• Use mole fraction, molar mass, and fractional volume of several different oxides to determine overall melt density.
• Convert between molar and volumetric units.
• Use partial molar volume, the coefficient of thermal expansion, and the coefficient of isothermal compressibility to calculate the molar volume of each oxide.
• Consider the influence of dissolved water on melt density.
• Develop a spreadsheet to carry out a calculation.
In the process the students will:
• Learn to use weight percent and molar mass to calculate mole fraction of each oxide.
• Increase their skill at unit conversions.
• Create XY scatterplots showing the relationship between density and temperature, pressure, and weight percent of water.
• Use partial derivatives to calculate molar volume of each oxide.

## Context for Use

Equipment: Each student or pair of students needs a computer with Excel and PowerPoint.

Classes: This module has been used in an Introductory Physical Volcanology course with upper level undergraduates.

In the class, the module was introduced during lab to be completed as homework due the following week. Students turned in hard-copies of the Excel spreadsheets and graphs, as well as their working Excel files. This worked well for junior and senior level students with excellent quantitative skills.

## Description and Teaching Materials

PowerPoint SSAC-pv2007.QE522.CC2.5-Student (PowerPoint 718kB Oct25 07)

If the embedded spreadsheets are not visible, save the PowerPoint file to disk and open it from there.

This PowerPoint file is the student version of the module. An instructor version is available by request. The instructor version includes the completed spreadsheet. Send your request to Len Vacher (vacher@usf.edu) by filling out and submitting the Instructor Module Request Form.

## Teaching Notes and Tips

This module, like the others in this collection, works best if coordinated with lecture and lab material.

If students have difficulty in getting their equations to produce the correct numbers in the orange cells – especially if their results are off by orders of magnitude – tell them to check their unit conversions. You cannot ever emphasize unit conversions enough.

Some students jump ahead to the end-of-module assignments without working through the main part of the module carefully. Those students have trouble.

## Assessment

The end-of-module questions can be used for assessment.

The instructor version contains a pre-test

## References and Resources

Spera, F., 2000, Physical properties of magma, In: Sigurdsson et al., eds., Encyclopedia of Volcanoes, Academic Press, 171-190. (a very useful paper that discusses the physical properties of magma in detail)

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