Wien’s law relates the temperature T of an object to the wavelength at which the object’s blackbody radiation spectrum peaks. (The Greek letter —lambda—is conventionally used to denote wavelength.) Mathematically, if we measure T in kelvins, we find that

Thus, at 6000 K (the approximate surface temperature of the Sun), the wavelength of maximum intensity is 0.29/6000 cm, or 480 nm, corresponding to the yellow-green part of the visible spectrum. A cooler star with a temperature of 3000 K has a peak wavelength of 970 nm, just longward of the red end of the visible spectrum, in the near infrared. The blackbody curve of a star with a temperature of 12000 K peaks at 242 nm, in the near ultraviolet, and so on.

We can also give Stefan’s law a more precise mathematical formulation. With T again measured in kelvins, the total amount of energy emitted per square meter of surface per second (a quantity known as the energy flux F) is given by

This equation is usually referred to as the Stefan-Boltzmann equation. (Stefan’s student, Ludwig Boltzmann, was an Austrian physicist who played a central role in the development of the laws of thermodynamics during the late nineteenth and early twentieth centuries.) The constant (the Greek letter sigma) is known as the Stefan-Boltzmann constant.

Notice just how rapidly the energy flux increases with increasing temperature. A piece of metal in a furnace, when at a temperature of 3500 K, radiates energy at a rate of about 850 W for every square centimeter of its surface area. Doubling its temperature to 7000 K (so that it becomes yellow to white hot, by Wien’s law) increases the energy emitted by a factor of 16 (four “doublings”), to 13.6 kilowatts (kW) (13,600 W) per square centimeter. Notice also that the law relates to energy emitted per unit area. The flame of a blowtorch is considerably hotter than a bonfire, but the bonfire emits far more energy in total, because it is much larger.

The SI unit of energy is the joule (J). Probably more familiar is the closely related unit called the watt (W), which measures power—the rate at which energy is emitted or expended by an object. One watt is the emission of one joule per second; for example, a 100-W lightbulb emits energy (mostly in the form of infrared and visible light) at a rate of 100 J/s. In these units, the Stefan-Boltzmann constant has the value