Solved this homework problem, but my answer is not the same as the professor's answer. Can someone solve this for me so I can check my work, please?
A titanium sphere, at 182°C, with a diameter of 0.002 m, density of 4,500 kg/m³, thermal conductivity of 21.9 W/mK, and specific heat of 522 J/kgK, is left to cool in air at 20°C with a heat transfer coefficient equal to 2 W/m²K. Considering convection as the only heat transfer mode between the sphere and the surroundings, estimate how long it will take for the sphere's temperature to reach 23°C and the total energy in the form of heat extracted from it. Justify your estimate.