# 32.5 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.

the definition of photon
8kg of a hot liquid initial T is 90°© is missed with another liquid 3kg at 20° calculate e équilibrium T
8kg of a hot liquid initial T is 90°© is missed with another liquid 3kg at 20° calculate e équilibrium T
Balki
Bright
what are the products when acid and base mixed?
Austin
salt and water
what work done
work done is the product of force and distance moved in the direction of force
Work done = force (F) * distance (D)
abdulsalam
what is resounance
Abdul
y
Tracy
explain the three laws of isaac Newton with the reference
1st law ; a body will continue to stay at a state of rest or continue to move at a uniform motion on a straight line unless an external force is been acted upon
Austine
3rd law; in every action there is an equal or opposite reaction
Austine
2nd law: F=ma
Austine
what is circut
newtons law of motion
hasiya
First law:In an inertial frame of reference, an object either remains at rest or continues to move at a constant velocity, unless acted upon by a force.
Manan
is the ability to do work
Energy
Nwany
u from
Hejreen
any body online hain
Hejreen
ability to do work is energy
what is energy
energy is ability of the capacity to doing work
shafiu
what is vector
A quantity that has both magnitude and direction
Donaldo
can a body with out mass float in space
mosco
Is the quantity that has both magnitude and direction
Amoah
Yes it can float in space,e.g.polyethene has no mass that's why it can float in space
Amoah
that's my suggestion,any other explanation can be given also,thanks
Amoah
A charge of 1.6*10^-6C is placed in a uniform electric field in a density 2*5^10Nc^-1, what is the magnitude of the electric force exerted on the charge?
what's phenomena
Phenomena is an observable fact or event.
Love
Prove that 1/d+1/v=1/f
What interference
What is a polarized light called?
Moyinoluwa
what is a half life
the time taken for a radioactive element to decay by half of its original mass
ken
mohammed
Half of the total time required by a radioactive nuclear atom to totally disintegrate
Justice
radioactive elements are those with unstable nuclei(ie have protons more than neutrons, or neutrons more than protons
Justice
in other words, the radioactive atom or elements have unequal number of protons to neutrons.
Justice
state the laws of refraction
Fabian
state laws of reflection
Fabian
Why does a bicycle rider bends towards the corner when is turning?
Mac
When do we say that the stone thrown vertically up wards accelerate negatively?
Mac
Give two importance of insulator placed between plates of a capacitor.
Mac
Macho had a shoe with a big sole moving in mudy Road, shanitah had a shoe with a small sole. Give reasons for those two cases.
Mac
when was the name taken from
retardation of a car
Biola
when was the name retardation taken
Biola
did you mean a motion with velocity decreases uniformly by the time? then, the vector acceleration is opposite direction with vector velocity
Sphere
what's velocity
mosco
Velocity is the rate of change of displacement
Divya