The amount of energy per second emitted by the object. Luminosity is an intrinsic physical property of an object. Brightness, however, depends on how far away the object is from the observer, as well as how luminous the object is. Brightness is proportional to the luminosity of the object and inversely proportional to the square of the distance. Continuous Spectra Bright Line Spectra Dark Line Spectra Kirchhoff's laws.
Wavelengths are characteristic of the chemical composition as well as the temp of the gas.
Blackbody absorbs and emits equally well at all wavelengths. The wavelength at which a blackbody emits the most radiation is inversely proportional to the temperature of the body. The relation is called Wien's Law . In the equation above, the constant sigma depends on the units you want your answer in. What's important then is not the value of the constant, but the proportionalities of the different variables.