A thermal process is being used to reduce the microbial population on production

contact surfaces of the packages needed for sterilization of the liquid product. The

spoilage microorganism has a D$121=10$ min and z $=8\backslash$deg C $.$ The microbial

population on the surface is $10$ per cm$2$ and the product contact surface area is $5$

cm$2/$package$.$ A $9$D process has been recommended.

$($a$)$ Determine the process time for containers at $140\backslash$deg C$.$

$($b$)$ Determine the number of containers with spoilage based on initial

survivors on the package surface with $1$ million packages filled.