Emissive Power, Emissivity and Stefan-Boltzmann law | Physics Grade XI

Emissive Power

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Emissive Power, Emissivity and Stefan-Boltzmann law | Physics Grade XI

Emissive Power, Emissivity and Stefan-Boltzmann law

Emissive Power
Emissive power of a body is defined the total energy of all wavelengths radiation per second per unit area of the body. Since the wavelength of radiation emitted ranges from zero to infinity,
     Emissive power, e = ∫0 eλ
 
Its SI unit is J m-2s-1 or Wm-2.
 
Emissivity
Emissivity of a body is the ratio of the emissive power of the body to the emissive power of the perfect black body at the same temperature. It is denoted by ε.
     Emissivity, ε = e/E
     or, e = εE
Where E is the emissive power of the perfectly black body at the same temperature as that of the given body.
 
Stefan-Boltzmann law
It states that the total amount of heat energy radiated per second per unit area of a perfectly black body is directly proportional to the fourth power of its absolute temperature. If E is the heat energy radiated per second per unit area of the surface of a black body of temperature T, then from Stefan’s law
          E α T4
     or, E = σ T4
where σ is the Stefan’s constant whose value is 5.67 * 10-8-watt m-2 K-4 in SI unit and 5.67 * 10-5 erg s-1cm-2 and E is the energy per second per unit area.
 
The energy per second or power radiated by an area A of the black body is
     P = E. A = σ. A. T4 ..…… (ii)
 
According to this law, all bodies radiate energy. Then, why do the bodies not lose all their thermal energy by radiation and cool down to 0 K? the answer is that they also absorb heat radiation from the surrounding objects and eventually come in thermal equilibrium with the environments. Suppose an object at absolute temperature T1 placed inside an enclosure of absolute temperature T0 (T1>T0).
 
Heat energy radiated per second per unit by the body is
     Eemit = σ T14
 
Heat energy absorbed per second per unit by the body is
     Eemit = σ T04
 
The net loss of heat energy,
     Enet = σ T14 - σ T04
           = σ (T14 - T04)
 
If the body is not perfectly black then,
     E = σ e (T1- T04), where e is the emissivity of the body
 
Prevost’s theory of Heat Exchange
According to this theory, everybody radiates heat radiation continuously at all temperatures and the quantity of heat radiated per unit area of the surface in unit time depends on the temperature of the body and not on the surroundings.
 
Applications of Heat Radiations
  1. White clothes are preferred in summer and dark-colored clothes in winter. When heat radiations fall on the white clothes, they reflect back but dark clothes absorb the heat which makes a person feel warmer.
  2. Polished reflectors are used in electric heaters to reflect maximum heat in the room

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