ताप संचरण - विकिरण

Heat Transfer by Radiation

• Heat radiation is electromagnetic waves with wavelengths ranging from 3 cm to 7800 Å.
• A medium is not required for transfer by this method.
• The speed of radiation in vacuum is C.
• This is the fastest method of heat transfer.
• Properties of heat radiation are similar to those of light.
• Intensity (I) is the rate of heat energy flowing perpendicularly through a unit area.
• Unit: joule/𝑚²𝑠𝑒𝑐 (SI), cal/cm²sec (cgs), or kcal/m²sec (mks).
• Total heat energy passing through area A in time t is Q = IAt.
• Power, P = Q/t = IA.
• The nature of a surface is determined by reflection (r), absorption (a), and transmission (t) coefficients.
• (r + a + t) = 1. This means that the sum of reflection, absorption, and transmission coefficients equals 1 for any surface.
• A perfect black body (PBB) has a = 1, so r = t = 0. Such a surface absorbs all incident radiation and reflects/transmits none.
• Emissive power is the amount of radiation emitted per unit area per unit time.
• The emissive power (E) for a black body and (e) for other objects, increases rapidly with temperature.
• Formula for total heat radiation from an area A in time t is Q = EAt (for PBB), Q' = eAt (for any object).
• Emissivity (ε) is the ratio of emissive power of an object to that of a perfect black body at the same temperature. ε = e/E and 0 < ε ≤ 1.
• Kirchhoff's Law states that at the same temperature, the ratio of emissivity and absorptivity for any object is equal to the emissivity of a perfect black body. ε = a.

Stefan-Boltzmann's Law

• Stefan-Boltzmann's Law states that the emissive power (E) of a perfect black body is directly proportional to the fourth power of its absolute temperature (T). E ∝ T⁴ or E = σT⁴.
• σ is the Stefan-Boltzmann constant, approximately 5.67 × 10⁻⁸ W/m²K⁴.
• For an object that is not a perfect black body, the law is modified to e = εσ T⁴.
• The net heat loss (ΔQ) from a body of area A at temperature T₁ to a surrounding environment at temperature T₂ is ΔQ′ = εσA (T₁⁴ - T₂⁴) (for any body). For a black body, it is ΔQ = σA (T₁⁴ - T₂⁴).
• Newton's law of cooling states that the rate of cooling of a hot object is proportional to the temperature difference between the object and its surroundings.

Planck's Law and related concepts

• Planck's law describes the spectral energy density of black body radiation as a function of wavelength and temperature.
• Wien's displacement law relates the peak wavelength of emission (λ𝑚𝑎𝑥) to the absolute temperature (T). λ𝑚𝑎𝑥 ∝ 1/T or λ𝑚𝑎𝑥 * T = b (Wien's constant ≈ 0.0029 m⋅K).
• The spectral energy density is maximum at a specific wavelength and is directly proportional to the fourth power of the absolute temperature.