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Problem 46 Hard Difficulty

The oceans have a volume of 317 million cubic miles and con- $\operatorname{tain} 1.32 \times 10^{21} \mathrm{kg}$ of water. Of all the hydrogen nuclei in this water, 0.0156$\%$ are deuterium. (a) If all of these deuterium nuclei were fused to helium via the first reaction in Equation 30.4 , determine the total amount of energy that could be released. (b) Present world electric power consumption is about $7.00 \times 10^{12} \mathrm{W}$ . If consumption were 100 times greater, how many years would the energy supply calculated in (a) last?

Answer

a. $3.61\times 10^{30} \mathrm{J}$
b. $1.63 \times 10^{8} y r$

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Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

Other Schools

Zachary M.

Hope College

Meghan M.

McMaster University

Video Transcript

in this question. We're basically looking at extracting deuterium from the water in the oceans and converting that into energy. Trudy Deuterium fusion reaction which forms hitem. Thank you, country. So first off we're ready to find is how many? Two tube down. And this will tell us how many events fusion events can occur. So, first off, we need to find number of water molecules. Total number of water molecules in the ocean can do that by taking the mess off the entire ocean, divided by the molar mess off. It's tool very multiplied it by Have a gradual is constant made a mess of the ocean we're given is 1.32 sent potent one kill glimpse The more I mess Yes, off water. It's 18 times that time on a stream. Programs for more. Multiply that by avocados. Clinton to give us the number of molecules. Now we can find how many hydrogen you kinda just simply two times the number of watermark use. Since issue what work it has to hydrogen, then we can continue to find the number of deuterium. It is recommended percent each off all hydrogen atoms, which are due to that is still points your 156 So you want to buy that friction? What percentage? By the number of hydrogen you should get what you eat sometimes. About 40 treat. No, we didn't look it. Now a fusion event number. Fusion's the chemical Be half the number off deuterium since each fusion reaction takes up, too new Turin's Finally you can get what is total energy release really active from? If we were to extract all the to tune from the oceans, then I mean, it told him on energy would be the number of fusion reactions. Bribe I. D. Energy that is released perfusion event that is three point 27 MTV and we wanted to cover day to S O units, which is Jews multiply by 1.6 times 10 apartments. 13 Jews For MTV or finance. There will be 3.61 time stamp off 30 jokes no, to calculate how much or how long this energy will last for off were given. Daddy consumption currently is about seven times in about shelf. But let us assume if the construction is 100 times greater, so the consumption power consumption would be 10 to power. 14. What? Quantify how long this would be able to last time that you will last. You take the energy of a power that is 3.61 cent party fight by 7% power off teeth. This is Joe's, but power symptoms off juice per second. So what do you get your way? Here's in terms of seconds, but the magnitude all the amenities quite high. So that's covered a two years. So we divide that by the normal seconds in a year that is 3.156 times and about seven seconds in a year. And we should get the number of juice. Yeah, 16 times. Enter Paul. Eat. Yes.

National University of Singapore
Top Physics 103 Educators
Christina K.

Rutgers, The State University of New Jersey

Farnaz M.

Other Schools

Zachary M.

Hope College

Meghan M.

McMaster University