Question

A white dwarf star has a mass of (10)30 kg and its luminousity is (10)24 (j)/s . Calculate how long it can survive with its present luminosity of its internal temperature is (10)7 k .

Answer 1

Answer on Question #45876 – Physics – Astronomy – Astrophysics

Question:

A white dwarf star has a mass of $10^{30}$ kg and its luminosity is $10^{24}$ J/s. Calculate how long it can survive with its present luminosity of its internal temperature is $10^{7}$ K.

Answer:

The lifetime of stars is approximately proportional to M/L (mass/luminosity ratio).

$$M_{\mathrm{sun}} / L_{\mathrm{sun}} \sim \text{lifetime of sun}$$ $$M_{\mathrm{white~dwarf}} / L_{\mathrm{white~dwarf}} \sim \text{lifetime of white dwarf}$$ $$M_{\mathrm{sun}} = 1.988 \times 10^{30} \mathrm{~kg}$$ $$L_{\mathrm{sun}} = 384.6 \times 10^{24} \mathrm{~J/s}.$$

The lifetime of sun is approximately $10^{10}$ years.

We can make the following proportion:

$$1.988 \times 10^{30} \mathrm{~kg} / 384.6 \times 10^{24} \mathrm{~J/s} = 10^{10} \mathrm{~years}$$ $$10^{30} \mathrm{~kg} / 10^{24} \mathrm{~J/s} = X \mathrm{~years}$$ $$\text{Then, } X = 10^{10} \cdot \frac{10^{30}}{10^{24}} \div \frac{1.988 \cdot 10^{30}}{384.6 \cdot 10^{24}} = 10^{10} \cdot \frac{10^{30} \cdot 384.6 \cdot 10^{24}}{10^{24} \cdot 1.988 \cdot 10^{30}} = 193.5 \cdot 10^{10} \mathrm{~years}$$

Answer: $193.5 \cdot 10^{10}$ years

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