SE3500 Tutorial 5 Plutonium formation and use. Data: For 235U ?capture235 =101 b ; ?f235 = 579 b For 238U ?a238 = 2·72 b For 239Pu ?capture239 = 271 b ; ?f239 = 749 b A reactor contains U kg of 235U, P kg 239Pu H kg of 238U The neutron flux is ? × 1016 neutrons m-2s –1 We consider for the present question U and P varying with time but ? and H as constant. Take ? = 10 and H = 100 103 kg Q1 Show that the rate of loss of 235U is given by dU dt = – k1 ? U in kg/thousand hours where k1 = 0·00245 Q2 Show that the rate of loss of 239Pu is given by dP dt = – k2 ? U in kg/thousand hours and determine the value of k2. Q3 Show that the rate of creation of 239Pu is k3 ? H in kg/1000 hrs and determine the value of k3 Q4 Prove that in this case if P(0) = 0 and U(0) = 715 U(t) = 715 exp(– 0·02445 t) and P(t) = 266·7 [1 – exp(– 0.245 t) ] with t in units of 1000 hrs. Make a sketch graph showing how P(t) and U(t) vary with time. Q5 Find the power outputs at the start and after 1 year, After one year what is the ratio of power from 239Pu to that from 235U fissions ?