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Small spherical particles of diameter D = 50 μm contain a fluorescent material that, when irradiated with white light, emits at a wavelength corresponding to the material’s temperature. Hence the color of the particle varies with its temperature. Because the small particles are neutrally buoyant in liquid water, a researcher wishes to use them to measure instantaneous local water temperatures in a turbulent flow by observing their emitted color. If the particles are characterized by a density, specific heat, and thermal conductivity of ρ = 999 kg/m3, k = 1.2 W/m ∙ K, and cp = 1200 J/kg ∙ K, respectively, determine the time constant of the particles.
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