(b) State and explain Stefan-Boltzmann's law.

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Another Explanation (5):

Stefan-Boltzmann's Law states that the total energy radiated per unit surface area of a black body across all wavelengths per unit time (the power radiated per unit area) is directly proportional to the fourth power of the black body's thermodynamic temperature T.

Mathematically: P/A = σT⁴

where:

P/A is the power radiated per unit area (W/m²)
σ is the Stefan-Boltzmann constant (5.67 x 10^-8 W/m²K⁴)
T is the absolute temperature (in Kelvin)

This means a hotter object radiates energy much more intensely than a cooler one.

(f) Calculate the surface temperature of sun and moon given that \( \lambda_m = 4753 \text{\AA} \) and \( 14 \mu \text{m} \) respectively, \( \lambda_m \) being wavelength of maximum intensity of emission.
(d) Calculate the maximum amount of heat which may be lost per second by radiation from a sphere of 5 cm in diameter at a temperature of 600 K when placed in an enclosure at a temperature of 300 K. Given that, \(\sigma = 5.7 \times 10^{-12} \, \text{watts/cm}^{-2}/(^\circ \text{C})^{-1}\).
(b) State Kirchhoff's law. From Stefan's law derive Newton's law of cooling. [6]
(xiii) State Stefan-Boltzmann law.
(4) The spectral energy curve of sunlight has a maximum at a wavelength of \(4.84 \times 10^{-7} \, \text{m}\). Assuming the Sun to be a black body,
(d) An aluminum foil of relative emittance 0.1 is placed in between two concentric spheres at temperatures 300 K and 200 K respectively. Calculate the temperature of the foil after the steady state is reached. Assume that the spheres are perfect blackbody radiators. Also calculate the rate of energy transfer between one of the spheres and the foil. [\(\sigma = 5.672 \times 10^{-8} \, \text{M.K.S. units}\)]
(b) What is the energy density of the Sun's radiation?
(j) State Wien’s displacement law.
(c) What is the wavelength of maximum intensity radiation radiated from a source at temperature \(3000^\circ \text{C}\)? (Wien's constant \(b = 0.288 \, \text{cm} \cdot \text{K}\)).
(5) Two large closely spaced concentric spheres (both are black body radiators) are maintained at temperatures of 200 K and 300 K respectively. The space in between the two spheres is evacuated. Calculate the net rate of energy transfer between the two spheres. [Given: \(\sigma = 5.672 \times 10^{-8} \, \text{W/m}^2\text{K}^4\)]
(c)Calculate the surface temperature of sun and moon given that \( \lambda_m = 4753 \, \text{Å} \) and 14 \(\mu \text{m}\) respectively, \( \lambda_m \) being wavelength at the maximum intensity of emission.
(h) Calculate the energy radiated per minute from the filament of an incandescent Lamp at 1500 K if the surface area is \(4.5 \times 10^{-5} \, \text{m}^2\) and its relative emittance is \(0.65 \, (\sigma = 5.672 \times 10^{-8} \, \text{W/m}^2\text{K}^4)\).
f) If a blackbody at temperature 6174 K emits 4700 Å with maximum energy, calculate the temperature at which it will emit a wavelength of \(1.4 \times 10^{-3}\) m with maximum energy.
(g) A black sphere of diameter 4 cm is heated to 400 K when the surrounding temperature is 300 K. What is the rate at which energy is radiated? Given \( \sigma = 6 \times 10^{-8} \, \text{Wm}^{-2} \, \text{K}^{-4} \).
(d) If a black body at temperature \(6174 \, \text{K}\) emits \(4700 \, \text{Å}\) with maximum energy. Calculate the temperature at which it emits a wavelength of \(1.4 \times 10^{-3} \, \text{m}\) with maximum energy.
(a) What is the temperature of its emitting surface?
(c) A black body at temperature 4980 K emits radiation of wavelength 4000 Å with maximum energy. Calculate the temperature at which it will emit a wavelength of \(1.45 \times 10^{-5} \, \text{cm}\) with maximum energy.
(d) Calculate the maximum amount of heat which may be lost per second by radiation from a sphere of 5 cm in diameter at a temperature of 600 K when is placed in an encloser at a temperature of 300 K. Given that \(\sigma = 5.7 \times 10^{-12} \, \text{watts/cm}^{-2} / (\circ C)^{-4}\).
b) Derive Wien's law of energy distribution.
(k)What is Stefan-Boltzmann law? State Wein's displacement law.