What's So Hot About Io?

• The Liquid Crystal IR Detective activity is appropriate for elementary and middle school students. Students should work in groups of two or more. Have them take turns being the "infrared detective."
• Review the electromagnetic spectrum, pointing out the major categories of radiation (radio, infrared, visible, ultraviolet, microwave, etc.) Introduce students to different temperature scales, including Kelvin. This will become relevant for question 2 as well as the Prometheus activity.
• Sheets of liquid crystal are available at many science museums and nature stores, or through a science supply catalog.

Answers to Questions:

1. There should be two hot spots visible.
2. The infrared detector is only sensitive to a small range of temperatures. Make sure students understand that, although one of the coins or tiles is at 0 Celsius, it still gives off heat (this is 273 Kelvin, well above "absolute zero").
3. The higher the temperature, the greater the area.
4. Answers will vary.

 Activity 2 - The Power of Prometheus!

• WARNING! Because of the complex mathematical equations, the Prometheus activity should be reserved for high school students or very advanced middle school students.

It does not matter which wavelength (from the x axis) is chosen, as long as a measurable power output can be determined from the y axis. Suggest that a wavelength between 3.5 and 5 microns is used. Each different value of wavelength will produce a different value of P_m from equation 1. However, when these values are used to calculate area the area values should be the same (about 233 Watts per square meter per micron.) This is because the ratio of values P_m and P for the same wavelength is constant.

What is the area of the volcano in square kilometers (A_km)? We know that something at 461 K emits 233 Watts per m² per micron. This is the energy output for a unit area (1 m²) at the selected wavelength of 5 microns. We know from the figure what the total output from all of Prometheus at 5 microns is, so we can determine the area of Prometheus by asking the question, how many times larger than 233 W (at 5 microns) is the total output (at 5 microns)? This is the number of square meters of the Prometheus volcano. At 5 microns, the power output from the volcano is P_, measured from the y axis and found to be 3.43 x 10⁹ Watts per micron. If radiating at 233 Watts per micron from every square meter of surface, the area of the volcano is P / P_m = 1.47 x 10⁷ m², = 14.7 km².

Find P_T. The figure in this equation, 5.67 x 10^-8 W m^-2 K^-4 is the Stefan-Boltzman constant. The total power from Prometheus is the sum of the power output at all wavelengths. The area has been determined from equation 2. The figure for area in square meters must be used in equation 3. Using a value of 461 K for T and 1.47 x 10⁷ for A_m:

P_T = 5.67 x 10^-8 x (461)⁴ x 1.47 x 10⁷ = 3.77 x 10¹⁰ Watts. This is nearly 40 billion Watts!

How many light bulbs does this hot spot represent? This is equivalent to 377 million light bulbs! The power coming out of the Prometheus volcano could light up every house in the United States (assuming 100 million homes in North America, each home could have 3 or 4 lights on simultaneously).

How do these figures compare? Io generates (from natural sources) about 140 times as much energy as the United States (from all of its power stations, mostly coal, gas and nuclear power plants.) Prometheus, one of many volcanoes on Io, generates about 1/18^th of the power capacity of the United States.

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This module was written by Brian Exton (National Optical Astronomy Observatories, Tucson AZ).

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Galileo Solid State Imaging Team Leader: Dr. Michael J. S. Belton

The SSI Education and Public Outreach webpages were originally created and managed by Matthew Fishburn and Elizabeth Alvarez with significant assistance from Kelly Bender, Ross Beyer, Detrick Branston, Stephanie Lyons, Eileen Ryan, and Nalin Samarasinha.

Last updated: September 17, 1999, by Matthew Fishburn

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