Introduction :
Mathematically P = `sigma` AT2 ., where A is the surface area, T is temperature of eh surface in Kelvin scale and `sigma` is the universal constant called Stefan's constant and its value is 5.670 x0 10-8 W / m2 K4 .
Stefan's law involved the temperature in Kelvin scale not in Centigrade scale. The fourth power of temperature indicates how sensitive the power emitted by a body to temperature changes. Initially Stefan concluded that the above equation is valid for any body as he did not perform experiments with black bodies. Later Boltzmann on the basis of principles of thermodynamics showed that the equation is valid only for black bodies. Hence the statement leading to the above equation is called Stefan-Boltzmann law.
P = e`lambda` `sigma` AT4 .........................(1)
where e`lambda` is emissivity of the body. Its value ranges from 0 to 1.
For a black body e`lambda` = 1 and for a perfect reflector e`lambda` = 0. For example, for polished aluminium e`lambda` = 0.05 as it is an excellent reflector , for soot (carbon black) e`lambda` = 0.95. Human skin has emissivity about 0.97 in infrared region of electromagnetic waves.
If a body with surface area A and temperature T is kept in surroundings with temperature Ts , it simultaneously emits and absorbs thermal radiation till dynamic thermal equilibrium is attained. Then the net rate of heat flow is given by
Pnet = Pemitted - Pabsorbed.
From equation (2) , Pemitted = e`lambda` `sigma` AT4 and Pabsorbed = e`lambda` `sigma` AT4s .
Hence Pnet = e`lambda` `sigma` AT4 - e`lambda` `sigma` AT4s = e`lambda` `sigma` A(T4 - T4s ).
After the thermal equilibrium is attained, the body and the surroundings are at the same temperature, the body emits the energy at the same rate as that it absorbs. Hence Pnet = 0.
If T > Ts the body emits more thermal radiation than it absorbs.
If T < Ts the body absorbs more thermal radiation than it emits.
The
emission of electromagnetic waves at the expense of the internal energy
of the bodies is known as thermal radiation. Theoretical explanation of
the nature of black body radiation finally led to the concept of energy
quanta which is the first step toward quantum mechanics enabling us to
investigate the secrets of atomic structure and other properties of the
substances.
Mathematical Equation for Stefan Boltzmann Law Radiation
oseph Stefan analysed the experimental data about the radiation of the bodies at various temperature and concluded that Emissive power of a (black) body is proportional to the forth power of the absolute temperatureMathematically P = `sigma` AT2 ., where A is the surface area, T is temperature of eh surface in Kelvin scale and `sigma` is the universal constant called Stefan's constant and its value is 5.670 x0 10-8 W / m2 K4 .
Stefan's law involved the temperature in Kelvin scale not in Centigrade scale. The fourth power of temperature indicates how sensitive the power emitted by a body to temperature changes. Initially Stefan concluded that the above equation is valid for any body as he did not perform experiments with black bodies. Later Boltzmann on the basis of principles of thermodynamics showed that the equation is valid only for black bodies. Hence the statement leading to the above equation is called Stefan-Boltzmann law.
Definition for Stefan-boltzmann Law Radiation
A body emits radiation that will be proportional to fourth power of absolute temperature and for any body Stefan-Boltzmann law can be given byP = e`lambda` `sigma` AT4 .........................(1)
where e`lambda` is emissivity of the body. Its value ranges from 0 to 1.
For a black body e`lambda` = 1 and for a perfect reflector e`lambda` = 0. For example, for polished aluminium e`lambda` = 0.05 as it is an excellent reflector , for soot (carbon black) e`lambda` = 0.95. Human skin has emissivity about 0.97 in infrared region of electromagnetic waves.
If a body with surface area A and temperature T is kept in surroundings with temperature Ts , it simultaneously emits and absorbs thermal radiation till dynamic thermal equilibrium is attained. Then the net rate of heat flow is given by
Pnet = Pemitted - Pabsorbed.
From equation (2) , Pemitted = e`lambda` `sigma` AT4 and Pabsorbed = e`lambda` `sigma` AT4s .
Hence Pnet = e`lambda` `sigma` AT4 - e`lambda` `sigma` AT4s = e`lambda` `sigma` A(T4 - T4s ).
After the thermal equilibrium is attained, the body and the surroundings are at the same temperature, the body emits the energy at the same rate as that it absorbs. Hence Pnet = 0.
If T > Ts the body emits more thermal radiation than it absorbs.
If T < Ts the body absorbs more thermal radiation than it emits.
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