Peak Wavelength and Total Emission

Any object above absolute zero radiates light across a whole range of wavelengths, called blackbody radiation. Wien's law says the wavelength where that radiation peaks, lambda_max, is inversely proportional to temperature: lambda_max = b/T, where b = 2.898 x 10⁻³ m K. Crank up the temperature and the peak shifts to shorter wavelengths, toward blue and violet. Cool the object down and the peak shifts to longer wavelengths, toward red and infrared. That is why a hotter star looks blue and a cooler one looks red: both emit a full spectrum, but the peak of that spectrum has slid to a different color.

Temperature also controls how much total energy pours out, not just what color dominates. The Stefan-Boltzmann law says power radiated per unit area scales as T^4. Double the temperature and the power per area jumps by a factor of 2⁴ = 16. This T⁴ dependence is steep: small temperature changes cause huge changes in brightness, which is why a modest rise in a star's surface temperature can make it dramatically more luminous.

These two laws connect color and brightness. Wien's law tells you where on the spectrum a star shines brightest, letting astronomers read off temperature just from color. Stefan-Boltzmann tells you how much energy that temperature produces overall. Together they explain why a hot blue star isn't just a different color than a cool red one, it is pouring out vastly more energy per unit surface area, tying directly back to the thermal motion of particles generating the radiation in the first place.