Stefan's Law

• What does Stefan's Law relate to?

  Power radiated by a perfect black body
• What are the two factors that affect the total power radiated by a perfect black body?

  Absolute temperature and surface area
• What does the Stefan-Boltzmann Law state about energy emission?

  Proportional to the fourth power of temperature
• What is the formula for calculating total power emitted according to Stefan's Law?

  P = σAT$^4$
• What does the symbol σ represent in the Stefan-Boltzmann Law?

  The Stefan-Boltzmann constant
• What does the variable A represent in the Stefan-Boltzmann equation?

  Surface area of the body
• What does the variable T represent in the Stefan-Boltzmann equation?

  Absolute temperature of the body
• How is the Stefan-Boltzmann Law applied in astronomy?

  To calculate luminosity of celestial objects
• What is the formula for the surface area of a spherical object?

  A = 4πr$^2$
• How does the Stefan-Boltzmann equation for luminosity of a star look?

  L = 4πr$^2$σT$^4$
• What does the variable L represent in the luminosity equation?

  Luminosity of the star
• What is the radius of the Sun denoted as?

  R
• What is the surface temperature of Proxima Centauri?

  3000 K
• What is the luminosity of Proxima Centauri?

  6.506 × 10$^23$ W
• What is the value of the Stefan-Boltzmann constant?

  5.67 × 10$^−8$ W m$^−2$ K$^−4$
• How do you rearrange the Stefan-Boltzmann equation for radius?

  R = L / (4πσT$^4$)
• What is the calculated radius of Proxima Centauri?

  1.061 × 10$^8$ m
• How do you find the ratio of the radii of Proxima Centauri and the Sun?

  R / R$☉$
• What is the radius of Proxima Centauri in solar radii?

  0.152 R$☉$
• What are the steps to calculate the radius of Proxima Centauri?

  1. List known quantities: T, L, σ, R$☉$
  2. Write Stefan-Boltzmann equation: L = 4πR$^2$σT$^4$
  3. Rearrange for radius: R = L / (4πσT$^4$)
  4. Substitute values and calculate
  5. Find ratio of Proxima Centauri's radius to the Sun's radius
• What are the implications of Stefan's Law in astrophysics?

  • Helps determine luminosity of stars
  • Relates temperature to energy output
  • Essential for understanding stellar evolution