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| Stefan-Boltzmann Law |
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| The energy of thermal radiation emitted per unit time by a black body of surface A, is given by |
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| u
= sAT2
-----(1) |
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| where s is a universal constant known as Stefan-Boltzmann constant and T is its temperature on absolute scale. The measured value of s is 5.67 x 10-8 W/m2 - K4. Equation (1) itself, is called the Stefan - Boltzmann law. Stefan had suggested this law from experimental data available on radiation and Boltzmann derived it from thermodynamical consideration. The law is also quoted as Stefan's law and the constant e is the Stefan constant. |
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| A body, which is not a black body, emits less radiation than given by equation (1). It is, however, proportional to T4. The energy emitted by such a body per unit time is written as |
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 -----(2) |
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| where e is a constant for the given surface having a value between 0 and 1. This constant is called the emissivity of the surface. It is zero for a completely reflecting surface and is unity for a black body. |
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| Using Kirchhoff's law, |
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| where a is the absorptive power of the body. The emissive power E is proportional to the energy radiated per unit time, that is, proportional to u. Using equations (1) and (2) in (3), |
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| Thus, emissivity and absorptive power have the same value. |
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| Consider a body of emissivity e, kept in thermal equilibrium in a room at temperature To. The energy of radiation absorbed by it per unit time should be equal to the energy emitted by it per unit time. This is because the temperature remains constant. Thus, the energy of the radiation absorbed per unit time is |
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| Now, suppose the temperature of the body is changed to T but the room temperature remains To, the energy of the thermal radiation emitted by the body per unit time is |
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| The energy absorbed per unit time by the body is |
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| Thus, the net loss of thermal energy per unit time is |
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