The total mass of the Sun is about 2×1030 kg, of which about 75 % was hydrogen w

Question

The total mass of the Sun is about 2×1030 kg, of which about 75 % was hydrogen when the Sun formed. However, only about 12 % of this hydrogen ever becomes available for fusion in the core. The rest remains in layers of the Sun where the temperature is too low for fusion.

a.) Use the given data to calculate the total mass of hydrogen available for fusion over the lifetime of the Sun.

b.) The Sun fuses about 600 billion kilograms of hydrogen each second. Based on your result from part A, calculate how long the Sun’s initial supply of hydrogen can last. Give your answer in both seconds and years.

c.) Given that our solar system is now about 4.6 billion years old, when will we need to worry about the Sun running out of hydrogen for fusion?

Explanation / Answer

part a )

total mass of sun = 2 x 10^30 kg

hydrogen mass = 2 x 01^30 * 0.75

available hydrogen = 12%

total mass of available hydrogen = 2 x 10^30 * 0.75 * 0.12 = 1.8 x 10^29 kg

part b )

rate of burning mass = 600 billion kg = 6 x 10^11 kg/s

lifetime = available mass/rate of buning = 3 x 10^17s

3 x 10^17s = 6.72 x 10^9 years

part c )

6.72 billion years - 4.6 billions = 2.12 billion years ,after we have to worry

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