p44_053.pdf

53. Since 1 . 00 L of water has a mass of 1 . 00 kg, the mass of the heavy water in 1 . 00 L is 0 . 0150

10 − 2 kg =

10 − 4 kg. Since a heavy water molecule contains one oxygen atom, one hydrogen atom and one

deuteriumatom,itsmassis(16 . 0u+1 . 00 u + 2 . 00 u) = 19 . 0u or (19 . 0 u)(1 . 661

10 − 27 kg / u) = 3 . 16

10 − 26 kg. The number of heavy water molecules in a liter of water is (1 . 50

10 − 4 kg) / (3 . 16

10 − 26 kg) =

10 21 . Since each fusion event requires two deuterium nuclei, the number of fusion events that

can occur is N =4 . 75

10 21 / 2=2 . 38

10 21 . Each event releases energy Q =(3 . 27

10 6 eV)(1 . 60

10 − 19 J / eV) = 5 . 23

10 − 13 J. Since all events take place in a day, which is 8 . 64

10 4 s, the power output

P = NQ

= (2 . 38

10 21 )(5 . 23

10 − 13 J)

=1 . 44

10 4 W=14 . 4kW .

8 . 64

10 4 s

1 . 50

4 . 75