Hot star -- loosely modeled on R136a1

Classical Mechanics Level 1

Please, read the notes section below before entering your answer.

This problem is an application of the Stefan-Boltzmann Law .

The value used for the Stefan-Boltzmann constant used was $5.6704\times 10^{-8} \frac{\text{Watts}}{(\text{Meters})^2\times (\text{degrees Kelvin})^4}$ .

Assume a spherical shape of the star and a radius of $2.0871\times 10^{10}$ meters to compute its surface area.

Assume a total power output of $3.\times 10^{33}$ Watts from the surface computed above.

What is the surface temperature rounded to an integer in kilo Kelvins?

Notes:

The requested answer is to be entered as an integer. Round your answer to the nearest kilo Kelvin, that is, divide the temperature in Kelvins by 1000, then add $\frac12$ to the result of the division and apply to that result, the floor (greatest integer in) function to get the final answer.

You can get an estimate of the desired answer by reading the R136a1 Wikipedia article.

This time, I avoided the using the metric (SI) prefixes as they seem to have caused confusion.

The answer is 56.

1 solution

A Former Brilliant Member
Feb 2, 2019

The area of a sphere with the specified radius is $5.47389\times 10^{21} m^2$ .

The power per square meter is $\frac{3.\times 10^{33} \text{Watts}}{5.47389\times 10^{21} m^2}$ or $5.48056\times 10^{11} \frac{\text{Watts}}{m^2}$ .

Dividing the previous result by the Stefan-Boltzmann constant, $5.6704\times 10^{-8} \frac{\text{Watts}}{(\text{Meters})^2\times (\text{degrees Kelvin})^4}$ , gives $9.66521\times 10^{18}\ (\text{degrees Kelvin})^4$ .

Computing the one-fourth power of the previous result gives $55757.4\ \text{degrees Kelvin}$ .

Dividing that result by 1000 gives 55.7574. Adding one-half gives 56.2574. Applying the greatest integer in the value function gives 56.

Hot star -- loosely modeled on R136a1

The answer is 56.

1 solution

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