Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

12 CHAPTER 2
theory of relativity. According to Einstein, the relationship between mass and energy
is
E = mc 2 , (2.23)
where E is the total energy of a piece of matter whose mass is m and c is the velocity of
light in vacuum. The principle of relativity tells us that all matter contains potential
energy by virtue of its mass. It is this energy source that is tapped to obtain nuclear
energy. The main virtue of this energy source is the vast amount of energy that can be
derived from conversion into its energy equivalent of small amounts of nuclear fuel.
W EXAMPLE 2.3
(a) How much energy can be obtained from 1gofnuclear fuel?
Solution
E = mc 2 = 1 × 10 −3 kg ×
3 × 10
8 m2
s
= 9 × 10 13 J.
Since there are 2.78 × 10 −7 kilowatt-hours (kW h) per joule, 1 g of nuclear fuel yields
13 J
kW · h
7 kW · h
E = 9 × 10 × 2.78 × 10−7 = 2.5 × 10
g J
g
(b) How much coal, whose heat content is 13,000 Btu/lb, must be burned to liberate
the same amount of energy as 1gofnuclear fuel?
Solution
1 Btu = 2.93 × 10 −4 kW h.
Therefore, the amount of coal required is
2.5 × 10 7 4 Btu
kW · h
kW · h = 1.3 × 10 × 2.93 × 10−4
lb Btu
3 lb
×2 × 10 × C tons
ton
Therefore,
C = 3280 tons (2981 metric tons)
The loss in mass accompanying ordinary energy transformations is not detectable
because of the very large amount of energy released per unit mass and the