How to measure the temperature of the sun
The Sunday Nation
Nairobi,
25 December 2011
A reader asked me this: “How hot is the surface of the sun?” My answer was equally short: “about 5,500 degrees Celsius”. But I knew that this was not what she really wanted to know. My guess is that she was wondering how the temperature is measured.
On first thought, you might think that you need to send a space-probe to the sun with a thermometer to take the measurement. Actually, you don’t: the temperature can be measured from right here on earth.
One method involves measuring of the intensity of the sun’s radiation on earth; that is, the power received per square metre. The best measurement is taken high up in the sky to avoid atmospheric interference.
Once we have the radiation intensity then we proceed as follows: We know that the sun is 150 million km away and it emits radiation equally in all directions – we have no reason to expect otherwise! So we can construct an imaginary sphere around the sun with a radius of 150 million km.
The intensity on any part of this sphere must be the same, therefore, it is possible to calculate the total power radiated by the sun. It is simply the power per square metre multiplied by the surface area of our imaginary sphere.
Now let’s use the real numbers: the radiation intensity is about 1,000watts per square metre; the surface area of the imaginary sphere is 4-pi-r-squared, that is, about 283 million-billion square kilometres.
Before doing any calculation, it is important to ensure that all measurements are consistent. Therefore we convert the intensity to watts per square kilometre, thus: 1,000 metres make one kilometre, therefore, 1,000 x 1,000 = 1,000,000sq-m make one sq-km. Consequently, 1,000W per sq-m are equal to 1,000,000 x 1,000 watts per square kilometre. That is, one billion watts per square kilometre.
Now we are ready to do the multiplication: one billion watts/sq-km times 283 million-billion sq-km, equals 283 million-billion-billion watts; or, if you prefer, 283 trillion-trillion watts. This is the total power radiated by the sun. Compare that to you domestic 100W bulb, and you begin to understand why it is impossible to look at the sun directly.
Once we know the total power radiated, the next step is to find out the radiation intensity on the surface of the sun. We do this by dividing the total power by the surface area of the sun – obviously, this is where all the energy is coming from!
The radius of the sun is about 700,000km, therefore its surface area is about 6,000,000,000,000 (six trillion) sq-km, or six million-trillion square metres. Dividing the total power by the surface area yields 47 million watts per square metre. This is the intensity of radiation at the surface of the sun (Phew: how nice it is to get back to a reasonable sounding number!).
We are now ready for the final step where we ask ourselves: what would be the temperature of a surface that emits 47 million W/sq-m? A not so complicated laboratory experiment can quickly give us the answer. It turns out to be about 5,500 degrees Celsius. QED
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