A white dwarf star has a mass of 10 kg 30 and its luminosity is 10 Js .24 −1 Calculate how long it can survive with its present luminosity if its internal temperature is .K 107
To determine the survival time of a white dwarf star with a given mass, luminosity, and internal temperature, we can use the concept of thermal radiation and the luminosity equation for a star. The luminosity of a star is primarily a result of the energy produced through nuclear reactions in its core. For a white dwarf, which is the remnant of a low to medium mass star, it no longer undergoes nuclear fusion but instead radiates its stored thermal energy over time.
The luminosity of a star is related to its surface temperature (T), radius (R), and Stefan-Boltzmann constant (σ) by the formula:
\[L = 4\pi R^2 \sigma T^4\]
where:
- \(L\) is the luminosity,
- \(R\) is the radius of the star,
- \(\sigma\) is the Stefan-Boltzmann constant (\(5.67 \times 10^{-8} \, \text{W m}^{-2} \, \text{K}^{-4}\)),
- \(T\) is the temperature in
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