Surgical implants are cylindrical pellets of powdered drug that are inserted into the body for controlled release of medication. These implants must be sterilized, and since they are water soluble, the drugs are sterilized using dry heat. To insure complete sterilization the pellets must be exposed to a temperature of at least \(140^{\circ} \mathrm{C}\) for 2 hours. Consider a testosterone implant \(1.0 \mathrm{in}\). long and \(0.3 \mathrm{in}\). in diameter. The drug has a melting point of \(152^{\circ} \mathrm{C}\) and so the oven temperature is set at \(145^{\circ} \mathrm{C}\). How long will sterilization take? The pellet is initially at \(25^{\circ} \mathrm{C}\) and its properties are:

\[ho=0.9 \mathrm{~g} / \mathrm{cm}^{3} \quad k=0.02 \mathrm{~W} / \mathrm{m} \mathrm{K} \quad C_{p}=2000 \mathrm{~J} / \mathrm{kg} \mathrm{K}\]

The heat-transfer coefficient in the sterilizer is \(h=10 \mathrm{~W} / \mathrm{m}^{2} \mathrm{~K}\).