The 74MW reactor of the NS Savannah had a range of 560000km

The 74-MW reactor of the NS Savannah had a range of 560000km at a speed of 20 knots for a single fuel loading. Compute the U₂₃₅ mass consumed for these specifications. (the answer is 60.7 kg)

Solution

Power P = 74 MW

             = 74 x10 6 W

Range R = 560000 km = 56 x10 ⁴ km

              = 56 x10 ⁴ x 10 ³ m

              = 56 x10 ⁷ m

Speed v = 20 knots

             = 20 x1.852 km / h           Since 1 knot = 1.852 km/h

             = 37.04 km/h

Time taken to travel given range t = R / v

                                                = 560000 km /(37.04 km/h)

                                                = 15118.79 h

                                                = 15118.79 x 60 x60 s           Since 1 hr = 60 min = 60 x60 s

                                                = 54.4276 x10 ⁶ s

Energy required E = Pt

                           = 74 x10 ⁶ x54.4276 x10 ⁶

                           = 4.0276 x10 ¹⁵ J

                           = ( 4.0276 x10 ¹⁵) /(1.6 x10 ^-19 ) eV

                           = 2.517 x10 ³⁴ eV

                           = 2.517 x10 ²⁸ MeV          Since 1 MeV = 10 ⁶ eV

We know average enenrgy released frm one fission of U 235 is E \' = 200 MeV

Number of fissions required to release E energy N = E / E \'

                                                                         = 1.2586 x10 ²⁶

Number of moles n = N/(6.023 x10 23 )

                            = 208.97 mol

We know 1 mole = 235 g

So, n moles = n x 235 g

                  = 49108 g

                  = 49.108 kg

Efficiency e = 80 %

So, required mass of U 235 is = 49.108 / 80 %

                                            = 49.108 / 0.8

                                            = 61.38 kg