What Wien's Law of Displacement Means for Infrared Saunas

How are Wien's Law and infrared saunas related? Two main types of infrared heaters can be used in infrared saunas - those that emit what is called "far infrared" energy and those that produce a slightly different type called "near infrared."

Well, we ordinary mortals might call the difference slight, but to a physicist the difference is significant.

You may have seen these two types of infrared mentioned in articles on our site, or you might have seen them referred to elsewhere. If you've been curious about the technical differences between them, fasten your seat belt, because this particular article will get into Wien's Law and what it means for infrared saunas. Although I’ll try to explain things as plainly as possible, expect some technical areas - it is physics, after all.

You probably already know that infrared energy is a radiant heat which warms your body directly instead of warming the air surrounding you. That's why a session inside an infrared sauna is much more comfortable than one inside a hot, steamy conventional sauna. Your skin is warmed, but the air you're breathing is not. But, you might be asking, what does this admittedly basic infrared sauna information have to do with Wien's Law?

Well, in order to truly understand the difference between far infrared and near infrared sauna heaters, we need to examine what Wien's Law (formally called Wien's Displacement Law) teaches. Wilhelm Wien, a German physicist, was the first scientist to study thermal radiation in depth. In 1893, he derived the thermodynamic principle that bears his name.

Expressed mathematically, here is Wien's Law:

Wien's Law

where λmax represents the peak wavelength, T is the black body's absolute temperature and b is equal to Wien's displacement constant, which is the number 2.8977685 (2898 microns).

Under Wien's Law, the wavelength of the peak of emission of a black body will be equal to 2898 microns divided by the temperature of the black body in kelvins (K). Therefore, the wavelength for maximal thermal radiation power can be calculated by dividing Wien's displacement constant (2.8977685 or 2898 microns) by the temperature as measured in kelvins.

As simply put as possible, Wien's Law states that the wavelength of the energy emitted by a source is inversely proportional to the temperature of the source. In other words, there is an inverse relationship between the wavelength of the peak of emission of a black body (a theoretically ideal object which is both a perfect emitter of electromagnetic radiation and a body that absorbs all incident electromagnetic radiation) and its temperature. The higher the object's temperature, the shorter the wavelengths will be at which it emits most of its thermal radiation.

Wien's Law and Infrared Sauna

So, how does Wien's Law relate to infrared sauna heaters? The websites of some infrared sauna sellers state, in essence, that the cooler the surface area of the sauna heater, the more far infrared energy that heater will produce.

Wien's Law confirms this statement, because "the wavelength of the peak of emission" will be a larger number (a longer wavelength, which means more far infrared energy) when the temperature of the black body (in this case, the infrared heater) is lower. The reverse is also true: when the temperature of the black body (the infrared heater) is higher, the wavelength of the peak of emission will be a smaller number (a shorter wavelength, which means more near infrared energy). So, if more near infrared energy is desired, the user should choose infrared heaters that operate at higher temperatures, but if more far infrared is the goal, infrared heaters operating at cooler temperatures should be used.

Infrared energy (including near and far) is categorized into different regions of the electromagnetic spectrum, based upon its wavelength:

  • Near infrared wavelengths fall between 0.75 and 1.40 micrometer (µm)
  • Short infrared wavelengths fall between 1.40 and 3.0 µm
  • Intermediate infrared (also called mid-wavelength infrared) wavelengths fall between 3.0 and 8.0 µm
  • Long-wavelength infrared wavelengths fall between 8.0 and 15.0 µm
  • Far infrared wavelengths fall between 15.0 and 1,000.0 µm

Any object, whether it's an infrared heater, the heating element of your stove, or the sun itself, radiates energy in a spectrum of wavelengths. Not a single wavelength, but a spectrum - a range of wavelengths. Consider the example of an infrared heater that radiates energy in a spectrum of wavelengths varying between 0.6 and 1.40 µm (the near infrared spectrum of wavelengths). Most of its energy might be radiated at a wavelength of 0.9 µm (for example), but it will also emit some energy at 0.6 µm. This emission at 0.6 µm is what allows us to see the red glow of the infrared heater as it's operating, because visible light falls within the 0.4 to 0.7 µm wavelength spectrum and the 0.6 µm infrared is inside that range.

The spectrum of light (with visible wavelengths of 0.4 to 0.7 µm) is even responsible for the names "infrared" and "ultraviolet." A wavelength of 0.4 µm will be visible as purplish-blue light, but the invisible wavelengths shorter than that are "above" the visible spectrum and so are called "ultra" violet light. A wavelength of 0.7 µm is visible as red light, but wavelengths longer than that are invisible because they fall "below" the visible spectrum. Those longer wavelengths are called "infra" red.

Heat always tries to distribute itself as evenly as possible, and a larger infrared heater has more surface area than a smaller heater. Because the heat produced by a larger heater will be distributed over a larger surface area, the overall surface temperature will be lower than that of a smaller heater (where the heat is concentrated on a smaller surface). And here, finally, is the bottom line regarding what Wien's Law means for infrared saunas: infrared heaters with lower surface temperatures will produce more far infrared energy.

More reading on Wien's Law and infrared heaters.

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