Explain how a star's colour and peak emission frequency can be used to determine its surface temperature, and describe what happens to the peak emission frequency of a star as its surface temperature increases.

A star can be treated as a black body, so its spectrum follows Planck’s law. The wavelength (or frequency) at which the intensity is greatest is the peak emission. By measuring the star’s colour – blue/white for hot stars, red for cool stars – and using the wavelength of the peak, one can apply Wien’s displacement law,

λ_max = b/T

or

ν_max = kT,

to calculate the surface temperature T. Thus the colour gives a qualitative indication of temperature, while the precise peak frequency provides a quantitative value.

As the surface temperature rises, Wien’s law shows that ν_max increases (or λ_max decreases). Therefore the peak of the spectrum shifts to higher frequencies, moving from the red/infrared part of the spectrum toward the blue/ultraviolet end.

Because the star is in thermal equilibrium, the power it radiates equals the power it absorbs, so its temperature remains stable once this balance is achieved.