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Using Radiation to Investigate Stars

Finding the radius and temperature of a star

  • 3 things to know
  • AS Unit 1

Overview

Recall questions on Finding the radius and temperature of a star.

What you need to know

Answer each one before you reveal it.

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Key term

Give Stefan's law for the total power radiated by a star, defining every symbol.

Key term

State the value and unit of the Stefan constant.

Key term

Rearrange Stefan's law to give the radius of a star.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Give Stefan's law for the total power radiated by a star, defining every symbol.

    Model answer

    L = 4πr²σT⁴, where L is the luminosity in watts, r the radius of the star in metres, σ the Stefan constant and T the surface temperature in kelvin.

  2. 2

    State the value and unit of the Stefan constant.

    Model answer

    5.67 × 10⁻⁸ W m⁻² K⁻⁴.

  3. 3

    Why does the temperature appear to the fourth power?

    Model answer

    The power radiated per unit area of a black body rises as the fourth power of the absolute temperature. That is what Stefan's law states.

  4. 4

    What happens to the luminosity if a star's surface temperature doubles at constant radius?

    Model answer

    It becomes sixteen times as great, since the fourth power of two is sixteen.

  5. 5

    What happens to the luminosity if the radius doubles at constant temperature?

    Model answer

    It becomes four times as great, since the surface area is proportional to the square of the radius.

  6. 6

    Rearrange Stefan's law to give the radius of a star.

    Model answer

    r = √(L/(4πσT⁴)), which needs the luminosity and the surface temperature.

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