In a manufacturing process, a spherical ceramic particle of diameter \(D=300 \mu \mathrm{m}\) and initial temperature \(T_{i}=1100 \mathrm{~K}\) is injected into a chamber containing a hot gas stream at \(T_{\infty}=1200 \mathrm{~K}, h=500 \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\). The particulate material has a density of \(ho=2500 \mathrm{~kg} / \mathrm{m}^{3}\), specific heat \(c=750 \mathrm{~J} / \mathrm{kg} \cdot \mathrm{K}\), thermal conductivity \(k=\) \(1.4 \mathrm{~W} / \mathrm{m} \cdot \mathrm{K}\), and emissivity \(\varepsilon=0.94\). The surroundings temperature is controlled by externally heating or cooling the chamber walls. Determine the particle temperature at \(t=0.1 \mathrm{~s}\) for \(T_{\text {sur }}=750 \mathrm{~K}, 850 \mathrm{~K}\), and \(950 \mathrm{~K}\). Plot the particle temperatures at times \(0 \leq t \leq 0.5\mathrm{~s}\) for the three surroundings temperatures.