10.11. The temperature history of the heating and cooling of a 40,000-1 tank during sterilization of medium is: 0 to 15 min, T= 85C; 15 to 40 min, T= 121C; 40 to 50 min, T= 85C; 50 to 60 min, T = 55C; > 60 min, T = 30C. The medium contains vitamins, the most fragile of the vi- tamins has an activation energy for destruction of 10 kcal/g-mol, and the value of a (see eq. 10.18) is 1 10* min. Assume vitamin destruction is first order and the initial concentration is 50 mg/l. R is 1.99 cal/g-mol-K. The medium contains 2.5 10' spores/l. The spores have an Eod = 65 kcal/g-mol, and ka at 121C is 1.02 min!. Estimate: (a) the probability of a suc- cessful sterilization, and (b) what fraction of the vitamin remains active?