Of all the hydrogen in the oceans, 0.0300% of the mass is deuterium. The oceans

Question

Of all the hydrogen in the oceans, 0.0300% of the mass is deuterium. The oceans have a volume of 320 million mi3. (Enter your answer using one of the following formats: 1.2e-3 for 0.0012 and 1.20e+2 for 120..) (a) If nuclear fusion were controlled and all the deuterium in the oceans were fused to42He, how many joules of energy would be released? (J) (b) World power consumption is about 7.00 1012 W. If consumption were 80 times greater, how many years would the energy calculated in part (a) last? (yrs)

Explanation / Answer

Density of water = 1000 kg/m3

mass of water on earth = 320 x 106 x (1609.34)3 x 1000 kg

mass of hydrogen in this water = (1/9) x 320 x 106 x (1609.34)3 x 1000 kg

mass of deuterium on earth = (1/9) x ( 0.030 / 100 ) x 320 x 106 x (1609.34)3 x 1000 = 0.444 x 1017kg

1 kg of Deuterium gives 3.38 x 1014 J

(a) total energy given by all the water on earth E = 0.444 x 3.38 x 1031 J = 1.50 x 1031 J

(b) divide the above E with 7 x 1012 x 120 x 365 x 86400

time = 566246285.4 = 0.566x 109 year

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