In the canning process, sealed cans of food are sterilized with pressurized steam in order to kill any microorganisms initially present in the food and thereby prolong the shelf life of the food. A cylindrical can of food has a diameter of 4 cm and length of 10 cm. The food material has a heat capacity of 4000 J/kg · K, a density of 1500 kg/m³, and thermal conductivity of 0.6 W/m · K. In the present process, steam, at 120°C, is used to sterilize the can. The convective heat-transfer coefficient is 60 W/m² · K. Initially, the can and its contents are at a uniform temperature of 20°C.

a. If the heat-transfer resistance offered by the can itself is neglected, and the can ends are thermally insulated, how long will it take for the center of the can to reach a temperature of 100°C, which is sufficient to kill all microorganisms?

b. What is the required time if the ends of the can are not sealed?

c. What will be the center temperature of the can and contents after 2500 seconds have elapsed?