# Black Body Radiation sample essay

When solid objects are heated, they emit radiation. At normal temperature, we are not aware of this radiation because the intensity is low. At higher temperatures, there is sufficient infrared radiation that we can feel the “heat” if we are close to them. At even higher temperature, the objects actually glow, like the heating element of toaster or red-hot electric stove burner.

Since they are radiating energy, there must be a rate at which they are radiating. They may radiate 10 Joules per second or maybe 100 Joules per second. This rate is related to the temperature of the object. It’s obvious that higher the temperature, they higher will be the rate of radiation. What may not be obvious is that the rate of radiation is proportional to the fourth power of temperature. Also, the bigger the object, higher the radiation. So the rate is proportional to their surface area. And the equation for this relation (Called Stefan-Boltzmann Equation) is,

Here is a universal constant known as Stefan-Boltzmann constant. The factor is called emissivity, is a number between 0 and 1. This depends on the characteristics of surface of radiation material.

The color of the light emitted by the hot object is also related to temperature. As the temperature increases, the electromagnetic radiation reaches a peak at higher frequency. An ideal black body would release all kinds of radiation when heated but the peak radiation depends on the temperature. It is found experimentally that the wavelength at the peak of the spectrum, is related to Kelvin temperature by

This is known as Wien’s Law.

Let me clear it with an example. Assume that Sun act as a black body and emits light whose peak intensity occurs in the visible spectrum at around 500nm. Putting this value on that equation gives Sun’s surface temperature which is 6000K.

Intensity as a Function of Wavelength at Different Temperatures

As you can see, as the temperature increases the intensity increases. And wavelength at which the radiation peaks decreases as the temperature increases.

A major problem facing scientists in the 1890s was to explain blackbody radiation. Maxwell’s electromagnetic theory had predicted that oscillating electric charges produce electromagnetic waves, and the radiation emitted by a hot object could be due to the oscillations of electric charges in the molecules of the material. Two formulations was created based on this concep by Wien and Reyleigh-Jeans. Although this would explain where the radiation came from, it did not correctly predict the observed spectrum of emitted light.

In the year 1900 Max Planck made a new and radical assumption: that the energy of the oscillations of atoms within molecules cannot have just any value; instead each has energy which is a multiple of a minimum value related to the frequency of oscillation by . He proposed an empirical formula that nicely fits the data (called Planck’s Radiation Formula). The formula gives intensity as a function of wavelength at the temperature ,

Since Human body is operating at 310K, you can call it a hot object. So human body also radiates energy. And the peak wavelength of radiation can be found out by using Wien’s Law and we get, . This corresponds to wavelength of infrared. That means human body emits infrared radiation.

Also the rate at which human body radiates can be found out using Stefan-Boltzmann Equation. Temperature of human body is 310K, surface area is about 1.5m² and emissivity is about .7. Assume that the temperature of surrounding is about 300K. Then the net heat energy radiated by human body per second is,

This is the amount of energy how body dissipates in order to keep yourself warm.

To give you some feeling on how large 80W is, let’s calculate the total amount of energy you dissipate per day. And the energy that you’re dissipating in 24 hours is .

This is a huge number. Suppose you’re climbing to the 20 storeyed building ( ) and your mass is . Then the amount of work you have to do is . Although human body is not much efficient as mechanical movements but the amount of energy you require to keep your body warm is about 140 times larger than this energy.

Where does this energy come from? Of course foods! So the all the foods that you eat ultimately is required to keep your body warm. It only uses a little amount of energy for mechanical works.

Now . You will find in many diet charts that Human body require 1600 to 2000 Calories of food per day and now you can calculate this using physics!

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