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# Calculating a Planet’s Temperature

Shawn Brooks, UTS (University of Toronto Schools)
sbrooks@utschools.ca

With just a little coaxing, and a little help from their calculators, our grade 10 science students can use a simple energy-balance type of climate model to calculate the average temperature of a planet.

With this activity, your students will be able to calculate what the earth’s average surface temperature would be if it didn’t have a greenhouse gas containing atmosphere.

This one-period activity can show your students how the numerical value of Earth’s albedo (0.3) is very meaningful to our planet’s temperature! If you are looking to inject a little more physics into your Earth and Space Science: Climate Change unit, this might be the thing for you.

Several years ago I had a chance to chat with Dr. Paul Kushner in the McLennan Physical Labs at the University of Toronto. He pulled a book off his shelf and tried to explain to me the simple climate model that I now share with my SNC2D students.

At first this calculation looked heavy to me, but then I realized that this simple climate model could be very accessible to grade 10 science students (if I went slowly, and I showed them how to calculate the 4th root of a number — something their scientific calculator can do).

The key concepts in this activity are very accessible:
• The Earth blocks a circular area of the sun’s light (πr2)
• The Earth radiates heat to outers pace over its entire surface area (4πr2)
• The energy received by the Earth equals the energy emitted by the Earth (the idea of the Earth being in thermal equilibrium)
I wanted my students to explore the calculations on their own, without me doing the calculations for them. I wanted this activity to complement the group work we already do.

While I was trying to put all the pieces of this activity together in my head, I had a moment of inspiration from the POGIL activities that the chemistry and biology teachers at my school were using.

POGIL is an acronym that stands for Process Oriented Guided Inquiry Learning. If you are curious about POGIL activities, please check out their website. I have used many of their activities and I can recommend the structure that POGIL uses for 4-person group work. My students have chuckled at some of the “what not to do” group work videos that I have shown them in class (this is an example of such a video).

I chose to emulate my simple climate model activity after the POGIL activities that I had used in other lessons because I wanted to address the key concepts of this climate model one at a time (I wanted to go slowly). I also wanted the students to work in groups to ensure the participation of each student in each group, as best as I could. The POGIL process provides for all of these things.

If you try out this simple climate model with your grade 10 science classes, I think you will find your students having very focussed discussions related to climate change and the greenhouse effect. I typically use it towards the end of the unit. This activity can also be extended. The students may want to explore the how albedo can influence a planet’s temperature: by lowering the albedo from 0.30 to 0.29, for example.

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