Small spheres of radius r, density p, and specific heat capacity c are heated to a temperature of t; and dunked in a oil bath at tot) to induce a phase transition. if the temperature of the oil bath can be assumed to be a constant, and that the heat transfer from each sphere to the surrounding fluid can be thought of as independent of the presence of other spheres, find the expression for temperature t(t) as a function of time. assume that the heat transfer coefficient is h. for small enough spheres, the heat transfer coefficient can be approximated as h ~ find the time constant τ for spheres with r = 1 mm, ρ = 7000 kg/m3, c = 400 j/k/kg, how long does it take for the sphere to reach 100 °c if t-500 °c and too-25 °c r. koil = 0.2 w /m/k.