A Fery’s cavity is maintained at a uniform temperature of and has a circular aperture…

PHYSICS · Multi-part · CBSE · Physics · Thermal Properties of Matter · Thermal Properties of Matter

Problem

A Fery’s cavity is maintained at a uniform temperature of 1200 K1200\,\text{K} and has a circular aperture of diameter 2.0 mm2.0\,\text{mm}. (i) Calculate the wavelength at which the intensity of the radiation emerging from the aperture is maximum. Take Wien’s constant b=2.9×10−3 m Kb = 2.9 \times 10^{-3}\,\text{m\,K}. (ii) Assuming the aperture behaves as a perfect black surface, determine the total radiant power leaving the aperture. Use the Stefan–Boltzmann constant σ=5.67×10−8 W m−2 K−4\sigma = 5.67 \times 10^{-8}\,\text{W m}^{-2}\,\text{K}^{-4}. (iii) By what factor would the power in part (ii) change if the diameter of the aperture were doubled while all other conditions remained the same? Justify your answer mathematically.

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