Wien's displacement law states that the wavelength of the peak radiation emitted by a black body is inversely proportional to its temperature.

$\lambda$_max = peak wavelength (m)

T = temperature (K)

Stefan's law states that the total power output of a star is proportional to the fourth power of the star's surface temperature and is directly proportional to the surface area.

P = power (W)

$\sigma$ = Stefan constant = 5.67 x 10^-8 (W m^-2 K^-4)

A = surface area (m²)

T = temperature (K)

I = intensity (W m^-2)

P = power (W)

d = distance from the star (m)

Hotter stars have a peak wavelength in the blue or ultraviolet region.

Cooler stars have a peak wavelength in the red or infrared region.

Stefan's law tells us that a star's total energy output per unit time (or power) increases rapidly with an increase in temperature, specifically it is proportional to the temperature raised to the fourth power.

As temperature increases the peak wavelength decreases.

According to Stefan's law, as the temperature of a star increases, its total energy output increases dramatically, specifically it increases with the fourth power of the temperature.