A 1000MWe reactor is operating with a three-batch refueling scheme with which a fuel batch is discharged after three cycles' depletion in the core (i.e., a batch fuel is irradiated during three cycles before discharge). The core is comprised of 195 fuel assemblies and each fuel assembly is comprised of 264 fuel rods (fuel length is 366 cm). The thermal efficiency of this reactor is 34%. Assume that the cycle length (cycle operating length) including refueling interval is 13 months and capacity factor is 70%. Also it is assumed that the core is comprised of three regions (i.e., inner, middle, and outer regions of same volume) in which the fresh batch fuel is loaded in the outer region and then moves into middle and inner regions. The inner, middle, and outer regions generate 40%, 30%, and 30% of the total thermal power, respectively for every cycle. The heavy metal loading of a fresh batch is 30,000kg, Please answer the following questions : a. What is the specific power in W/g) for a fresh batch at BOC (beginning of cycle) of the first cycle ? b. What is the average linear power density (W/cm) at BOC of the first cycle ? c. What is the average burnup (MWd/kg) over all the batches at the end of the first cycle ? What is the average burnup (MWd/kg) of the fuel batch in the outer most region at the end of the first cycle? d. What is the discharge burnup (MWd/kg) of a fuel batch for an equilibrium cycle ? (Hint : Divide the total thermal energy generated by a batch during three cycles with initial heavy metal loading of the batch)