# 22.5 Fusion  (Page 5/12)

 Page 5 / 12

## Calculating energy and power from fusion

(a) Calculate the energy released by the fusion of a 1.00-kg mixture of deuterium and tritium, which produces helium. There are equal numbers of deuterium and tritium nuclei in the mixture.

(b) If this takes place continuously over a period of a year, what is the average power output?

Strategy

According to ${}^{2}\text{H}+{}^{3}\text{H}\to {}^{4}\text{He}+n$ , the energy per reaction is 17.59 MeV. To find the total energy released, we must find the number of deuterium and tritium atoms in a kilogram. Deuterium has an atomic mass of about 2 and tritium has an atomic mass of about 3, for a total of about 5 g per mole of reactants or about 200 mol in 1.00 kg. To get a more precise figure, we will use the atomic masses from Appendix A. The power output is best expressed in watts, and so the energy output needs to be calculated in joules and then divided by the number of seconds in a year.

Solution for (a)

The atomic mass of deuterium ( ${}^{2}\text{H}$ ) is 2.014102 u, while that of tritium ( ${}^{3}\text{H}$ ) is 3.016049 u, for a total of 5.032151 u per reaction. So a mole of reactants has a mass of 5.03 g, and in 1.00 kg there are $\left(\text{1000 g}\right)/\left(\text{5.03 g/mol}\right)\text{=198}\text{.}8 mol of reactants$ . The number of reactions that take place is therefore

$\left(\text{198.8 mol}\right)\left(6\text{.}\text{02}×{\text{10}}^{\text{23}}\phantom{\rule{0.25em}{0ex}}{\text{mol}}^{-1}\right)=1.20×{\text{10}}^{\text{26}}\phantom{\rule{0.25em}{0ex}}\text{reactions}.$

The total energy output is the number of reactions times the energy per reaction:

$\begin{array}{}E=\left(1.20×{\text{10}}^{\text{26}}\phantom{\rule{0.25em}{0ex}}\text{reactions}\right)\left(\text{17.59 MeV/reaction}\right)\left(1.602×{\text{10}}^{-\text{13}}\phantom{\rule{0.25em}{0ex}}\text{J/MeV}\right)\\ \text{}=3\text{.}\text{37}×{\text{10}}^{\text{14}}\phantom{\rule{0.25em}{0ex}}\text{J}\text{.}\end{array}$

Solution for (b)

Power is energy per unit time. One year has $3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{s}$ , so

$\begin{array}{lll}P& =& \frac{E}{t}=\frac{3\text{.}\text{37}×{\text{10}}^{\text{14}}\phantom{\rule{0.25em}{0ex}}\text{J}}{3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{s}}\\ & =& \text{}1\text{.}\text{07}×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{W}=\text{10}\text{.}7\phantom{\rule{0.25em}{0ex}}\text{MW}\text{.}\end{array}$

Discussion

By now we expect nuclear processes to yield large amounts of energy, and we are not disappointed here. The energy output of $3\text{.}\text{37}×{\text{10}}^{\text{14}}\phantom{\rule{0.25em}{0ex}}\text{J}$ from fusing 1.00 kg of deuterium and tritium is equivalent to 2.6 million gallons of gasoline and about eight times the energy output of the bomb that destroyed Hiroshima. Yet the average backyard swimming pool has about 6 kg of deuterium in it, so that fuel is plentiful if it can be utilized in a controlled manner. The average power output over a year is more than 10 MW, impressive but a bit small for a commercial power plant. About 32 times this power output would allow generation of 100 MW of electricity, assuming an efficiency of one-third in converting the fusion energy to electrical energy.

## Section summary

• Nuclear fusion is a reaction in which two nuclei are combined to form a larger nucleus. It releases energy when light nuclei are fused to form medium-mass nuclei.
• Fusion is the source of energy in stars, with the proton-proton cycle,

being the principal sequence of energy-producing reactions in our Sun.

• The overall effect of the proton-proton cycle is

where the 26.7 MeV includes the energy of the positrons emitted and annihilated.

• Attempts to utilize controlled fusion as an energy source on Earth are related to deuterium and tritium, and the reactions play important roles.
• Ignition is the condition under which controlled fusion is self-sustaining; it has not yet been achieved. Break-even, in which the fusion energy output is as great as the external energy input, has nearly been achieved.
• Magnetic confinement and inertial confinement are the two methods being developed for heating fuel to sufficiently high temperatures, at sufficient density, and for sufficiently long times to achieve ignition. The first method uses magnetic fields and the second method uses the momentum of impinging laser beams for confinement.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
How we can toraidal magnetic field
How we can create polaidal magnetic field
4
Because I'm writing a report and I would like to be really precise for the references
where did you find the research and the first image (ECG and Blood pressure synchronized)? Thank you!!