Watch Your Head Here Comes an Equation

Physicists have boiled this black-body curve business down to a couple of laws. Wien's law states that the wavelength of peak emission is proportional (the symbol a means "is proportional to") to 1 over absolute temperature as expressed in Kelvins:

Wavelength of peak emission a 1

temperature

This law puts into an equation what we have been saying in words. As something gets hotter, its peak wavelength gets smaller. The two are inversely proportional.

Don't worry, we'll discuss absolute temperature and Kelvins in Chapter 16. For now, just know that the hotter an object, the bluer its radiation, and the cooler an object, the redder its radiation.

It is also true that the total energy an object radiates is proportional to its temperature— in fact, it is proportional to the fourth power of the object's temperature:

Total energy radiated a temperature4

In other words, if you double the temperature of an object, say from 1000 K to 2000 K, it will radiate not twice the energy, but 16 times the energy (24, or 2 x 2 x 2 x 2 = 16). This relationship between energy radiated and temperature is called the Stefan-Boltzmann law.

Star Words

The Kelvin (K) temperature scale is tied to the Celsius (C) temperature scale, and is useful because there are no negative Kelvin temperatures. 0 C is the temperature at which water at atmospheric pressure freezes. 100 C is the temperature at which water boils. Absolute zero (0 K) is the coldest temperature that matter can attain. At this temperature, the atoms in matter would stop jiggling around all together. 0 K corresponds to approximately -273 C, and under laboratory conditions, temperatures in the milliKelvin (thousandths of a Kelvin) range can be attained. For a sense of scale, stars like the Sun have surface temperatures of about 6000 K. A warm day on Earth is about 300 K.

Star Words

The Kelvin (K) temperature scale is tied to the Celsius (C) temperature scale, and is useful because there are no negative Kelvin temperatures. 0 C is the temperature at which water at atmospheric pressure freezes. 100 C is the temperature at which water boils. Absolute zero (0 K) is the coldest temperature that matter can attain. At this temperature, the atoms in matter would stop jiggling around all together. 0 K corresponds to approximately -273 C, and under laboratory conditions, temperatures in the milliKelvin (thousandths of a Kelvin) range can be attained. For a sense of scale, stars like the Sun have surface temperatures of about 6000 K. A warm day on Earth is about 300 K.

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