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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300

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College Physics

11th Edition
Raymond A. Serway + 1 other
ISBN: 9781305952300
Textbook Problem

Measurements on two stars indicate that Star X has a surface temperature of 5 727°C and Star Y has a surface temperature of 11 727°C. If both stars have the same radius, what is the ratio of the luminosity (total power output) of Star Y to the luminosity of Star X? Both stars can be considered to have an emissivity of 1.0.

To determine
The ratio of the luminosity of Star Y to the luminosity of star X.

Explanation

Given info: Surface temperature of Star X is 5727°C and Surface temperature of Star Y is 11727°C and both the stars are of same radius.

Formula to calculate the net power radiated by the Star X is,

PX=σAeTX2

  • PX is the power radiated by the Star X,
  • σ is Stefan’s – Boltzmann constant,
  • A is the surface area of the Star,
  • e is emissivity of the Star,
  • TX is the surface temperature of star Y.

Formula to calculate the net power radiated by the Star X is,

PY=σAeTY2

  • PY is the power radiated by the Star X,
  • σ is Stefan’s – Boltzmann constant,
  • A is the surface area of the Star,
  • e is emissivity of the Star,
  • TY is the surface temperature of star Y.

Equate both power radiate equation.

PYPX=σAeTY2σAeTX2

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