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Using Radiation to Investigate Stars

Stefan's law, luminosity and stellar radius

  • 3 things to know
  • Component 2

Overview

Value of the Stefan constant and luminosity of a star.

What you need to know

Answer each one before you reveal it.

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Key term

State Stefan's law as an equation, defining every symbol and its unit.

Key term

Explain how a star can be far more luminous than the Sun while being much cooler at its surface.

Key term

What is the value of the Stefan constant?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    State Stefan's law as an equation, defining every symbol and its unit.

    Model answer

    The law is P = AσT⁴, where P is the total power radiated in watts (W), A is the surface area in m², σ is the Stefan constant in W m⁻² K⁻⁴ and T is the absolute temperature in kelvin (K).

  2. 2

    What is the value of the Stefan constant?

    Model answer

    The Stefan constant is σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴.

  3. 3

    Define the luminosity of a star.

    Model answer

    The luminosity of a star is the total power it radiates in all directions over all wavelengths, measured in watts.

  4. 4

    State the expression for the surface area of a star of radius R.

    Model answer

    A star of radius R is a sphere of surface area A = 4πR².

  5. 5

    Write Stefan's law in a form suitable for a spherical star.

    Model answer

    Combining the two gives L = 4πR²σT⁴, where L is the luminosity in watts and R is the star's radius in metres.

  6. 6

    By what factor does a star's luminosity change if its surface temperature is doubled at constant radius?

    Model answer

    The luminosity increases by a factor of sixteen, because it is proportional to the fourth power of the absolute temperature.

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