Assume that the temperature of the surface of the sun is 5000 K and the surface temperature of another virtual star is 2500 K. The power radiated by a virtual star is 30 times the power radiated by the sun. The radius

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Correct answer: D. 4 30 \,r_ sun

According to the Stefan-Boltzmann law, the power radiated by a black body is given by

P = \sigma A T^4 = \sigma (4 \pi r^2) T^4

.

For the sun:

P_{s} = \sigma (4 \pi r_{s}^2) T_{s}^4

For the virtual star:

P_{v} = \sigma (4 \pi r_{v}^2) T_{v}^4

Given

P_{v} = 30 P_{s}

, we have:

\sigma (4 \pi r_{v}^2) T_{v}^4 = 30 \sigma (4 \pi r_{s}^2) T_{s}^4

\dfrac{r_{v}^2}{r_{s}^2} = 30 \left( \dfrac{T_{s}}{T_{v}} \right)^4

Substituting

T_{s} = 5000

K and

T_{v} = 2500

K:

\dfrac{r_{v}^2}{r_{s}^2} = 30 \left( \dfrac{5000}{2500} \right)^4

\dfrac{r_{v}^2}{r_{s}^2} = 30 (2)^4 = 30 \times 16 = 480

r_{v} = \sqrt{480} r_{s} = 4\sqrt{30} r_{s}

Answer:

4\sqrt{30}\,r_{sun}

Assume that the temperature of the surface of the sun is 5000 K and...

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