Today:

• Energy from the Sun.

Why is the Sun such an important source of energy?

• The Sun has a high surface temperature.– 5800 K– Every bit of the Sun’s surface emits a tremendous

amount of radiation.

• The Sun is large.– Total area of radiating surface is immense

• A = 4r2 = 4(6.96x108 m)2 = 6.1x1018 m2

– The total amount of energy emitted every second by the Sun is huge.

• How big is huge?

Let’s do some math to find out just how big huge is.

Where does this energy come from?

• This question stumped scientists for centuries.

• Mystery deepened in 19th century when scientists found evidence that life had existed on Earth for hundreds of millions of years.

• Life depends on solar energy, so the Sun must be at least that old. What type of energy has kept the Sun shining that long?– We now know Earth is 4.56 billion years old.

Early explanations

• Contraction due to gravity should compress and heat the Sun.– Calculations showed that the Sun could be at

most 25 million years old, so this can’t be correct.

• Could burning (combustion) be the source?– No, and here’s why:

Combustion isn’t the answer

Chemical reactions in burning release ~10-19 joules per atom.

The number of atoms that would have to be combusted each second is:

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3.96 ×1026 J /s

10−19 J /atom= 3.9 ×1045 atoms per second

The Sun contains roughly 1057 atoms, so the length of time required to consume the entire Sun by burning is:

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1057 atoms

3.9 ×1045 atoms per second= 3 ×1011 seconds,

or about 10, 000 years.

This can’t explain how the Sun shines.

Einstein to the rescueIs there some process similar to burning that would release much more energy per atom? If so the rate of consumption could be decreased and the lifetime of the Sun would be consistent with the known age of life on Earth.

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E = mc 2

E = amount of energy in joules

m = quantity of mass in kg

c = speed of light in m/s

In 1905, Albert Einstein proposed that a quantity of mass m could be converted into an amount of energy E according to his now-famous equation:

Hints that this may work:

• The Sun isn’t very dense. This suggests it is made mainly of the lightest atoms -- hydrogen and helium.

• The center of the Sun is very hot, so these atoms would be completely ionized.

• Under these conditions hydrogen nuclei could fuse together to form helium.– Called hydrogen fusion or thermonuclear fusion.

Thermonuclear fusion

• The essence of thermonuclear fusion is the following reaction:– 4H He + energy

• How much energy does this reaction release?

• What happens exactly during thermonuclear fusion?

Will thermonuclear fusion work?

We know how much energy is released in each reaction, but we need to understand the rate at which the Sun would consume mass through thermonuclear fusion and compare it to the mass of the Sun to determine if this is a good explanation. Let’s do that now.

This is easily long enough to explain the Sun’s energy output and allow enough time for life to have developed.

In reality, the lifetime of the Sun will be about 11-12 billion years. Only a portion of the Sun is hot enough for thermonuclear fusion and not all of the hydrogen in the Sun will be burned before other stuff (that we’ll talk about in the next month or so) happens to end its life.