The sun radiates energy at the rate 3.8 ×10^26 W . The...

The sun radiates energy at the rate $3.8 \times 10^{26} \mathrm{W} .$ The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is $2.0 \times 10^{30} \mathrm{kg} .$ a. How much mass does the sun lose each year? b. What percentage is this of the sun's total mass? c. Estimate the lifetime of the sun.

The sun radiates energy at the rate $3.8 \times 10^{26} \mathrm{W} .$ The source of this energy is fusion, a nuclear reaction in which mass is transformed into energy. The mass of the sun is $2.0 \times 10^{30} \mathrm{kg} .$
a. How much mass does the sun lose each year?
b. What percentage is this of the sun's total mass?
c. Estimate the lifetime of the sun.

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Key Concepts

Energy-Mass Equivalence

This concept, encapsulated in Einstein’s equation E=mc², relates energy and mass, showing that mass can be converted into energy and vice versa. It provides a framework for understanding how nuclear fusion generates vast amounts of energy by transforming a small amount of mass into energy.

Luminosity

Luminosity is a measure of the total amount of energy a star emits per unit time, expressed in watts (joules per second). It is crucial for calculating the rate of mass loss in a star because it directly relates the energy output to the corresponding mass converted via fusion processes.

Nuclear Fusion

Nuclear fusion is the process by which light atomic nuclei combine to form a heavier nucleus, releasing energy in the process. This energy release occurs because of the mass difference between the reactants and the products, and it is the fundamental source of a star’s energy.

Stellar Lifetime Estimation

Estimating a star’s lifetime involves understanding the rate at which it loses mass through fusion (energy production) compared to its total mass. By calculating the annual mass loss and comparing it to the star's total mass, one can approximate how long the star can continue to fuse material before significant depletion occurs.

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