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Calculating the Temperature of the Earth

The mean temperature of the Earth can be calculated using the Stefan-Boltzmann law of radiation. Your students will understand how models of global warming can be constructed. SDG, 13,14 and 15.

Publisher: T³ Europe

Author: Ian Galloway

Topic:  Mathematics  Physics

The mean temperature of the Earth can be calculated using the Stefan-Boltzmann law of radiation.  This law features in the curriculum of many school physics curricula and states that the power of the radiation emitted per square metre by an object depends on the fourth power of the absolute temperature.   The model can be modified using the albedo and the cloud cover to arrive at a mean temperature of 11 °C.  This compares well to the accepted value of 14 °C  and a pre-industrial value of 13 °C.

The formulae lend themselves to the graphing calculator and modelling the albedo is a T3 activity.  The activity demonstrates the power of constructing a physical model in order to understand the processes taking place in a real situation, in this case the mean temperature of the Earth.  Students will realise that no account has been made of absorption of radiation by CO2 or CH4, both greenhouse gases which are being pumped into the atmosphere through human activity and the object of another T3 activity.  Students may be able to come up with their own estimates of the effects of these gases upon the global mean temperature.