Question

A white dwarf star has a mass of 1030 kg. Its luminosity is 1024 Js−1. Calculate how
long it can survive with its present luminosity if its internal temperature is 107 K.

Answer 1

Answer on Question#61094 – Physics – Astronomy – Astrophysics

A white dwarf star has a mass of $10^{30}$ kg. Its luminosity is $10^{24}$ Js-1. Calculate how long it can survive with its present luminosity if its internal temperature is $10^{7}$ K.

Solution. The amount of energy emitted will be equal to the amount of energy produced by fusion of hydrogen to helium over that lifetime. $E = mc^2$. Here $m$ is the amount of matter that was converted into energy. Hence total energy of the star equal

$$E = Mc^2 = 10^{30} \, kg \cdot \left(3 \cdot 10^8 \, \frac{m}{s}\right)^2 = 9 \cdot 10^{46} \, J.$$

Using luminosity definition we get lifetime for star $t = \frac{E}{L} = \frac{9 \cdot 10^{46}}{10^{24}} = 9 \cdot 10^{22} \, s \approx 2.85 \cdot 10^{15} \, \text{year}$.

Answer. $t = 9 \cdot 10^{22} \, s \approx 2.85 \cdot 10^{15} \, \text{year}$.

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