Plot the temperature as a function of time. One technique for detecting chemical threats uses a laser to ablate small particles so that they can subsequently be analyzed using ion mobility spectroscopy. The laser pulse provides energy to a particle according to: ˙qlaser = q˙ max exp[−(t−tp)2 2 td2 ] where q˙ max= 0.22 W is the maximum value of the laser power, tp = 2μs is the time at which the peak laser power occurs, and td = 0.5 μs is a measure of the duration of the pulse. The particle has radius rp = 5 μm and has properties c = 1500 J/kg-K, k = 2.0W/m-K, and ρ = 800 kg/m3 . The particle is surrounded by air at T∞ = 20◦C. The heat transfer coefficient is h = 60000W/m2 -K. The particle is initially at T∞.
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