Video Transcript
In this video, we will be
discussing geothermal power.
Now, just from the word
“geothermal,” we can get a good sense of what we’re talking about here: “geo”
relating to the earth and “thermal” relating to heat. In other words then, we’re talking
about heat generated deep within the earth. This heat that we’re talking about
is actually generated by the radioactive decay of unstable elements found deep
within the Earth. This ends up heating up and even
partially melting the rocks beneath the surface of the Earth, whether they’re the
rocks forming the crust of the Earth or the mantel.
Now, in some specific regions of
the Earth, such as regions with high volcanic activity, this partially molten rock —
this magma, as it’s called — can be found relatively close to the surface of the
Earth. And when water passes by these
extremely hot rocks, whether by natural processes or whether by pumping down from
the surface, the heat from the magma is transferred to the water; the water heats
up. Now, this hot water can come back
up to the surface of the Earth, once again, either by natural processes or by
pumping. And we can harness the heat from
the water. We can harness this energy and turn
it into electrical energy.
Now, in some cases, the water that
comes up to the surface of the Earth is just the perfect temperature to use for
therapeutic purposes too. Communal baths, like we saw on the
opening screen of this video, and hot springs are common uses for this kind of
water. Sometimes though, the water is hot
enough that it comes up to the surface as steam rather than liquid water. Now, there are different kinds of
geothermal power station. Some of them convert the hot water
coming up to the surface into steam directly. And some others use the heat from
the hot water or steam if it’s already coming up as steam to heat up another liquid,
which gets converted into steam. Either way, whichever liquid is
being converted into steam in this geothermal power station, that steam is then used
to turn a turbine. And that turbine is attached to a
generator, which produces electrical energy.
In other words then, the energy
conversions that occur, energy of thermal power station, are the following. Firstly, the internal energy of the
hot water or steam coming up from the Earth gets converted into kinetic energy as
the steam is used to turn the turbine. Now, because the turbine is
attached to the generator, the generator takes the kinetic energy of the turbine and
converts it into electrical energy. And at this point, that can be
carried off by the transmission grid to homes and businesses needing power.
Now, just like any other method
used to produce electrical power, geothermal power has its own advantages and
disadvantages. Its advantages include the fact
that it’s a renewable energy source. When we produce electrical energy
in a geothermal power station, we do not deplete or use up any fuel. The water that comes up from within
the earth can be pumped back down again. And in this way, the water can be
recycled. It can go back down and be heated
up again and then come back up to the surface of the Earth. Now, there’re certainly enough
radioactive material within the Earth to heat the rocks in the Earth faster than we
can extract energy from them. Therefore, in a geothermal power
station, we’re not using up any resources. And hence, it’s a renewable energy
source.
Secondly, although the building
process of a geothermal power station can result in the release of pollutants and
greenhouse gases, once a geothermal power station is built, it releases very few
pollutants and greenhouse gases. And in that respect, a geothermal
power station is better for the environment than a fossil-fuel-powered power
station. Now, the reason for this is that at
a geothermal power station, there is no fuel being burnt. As we’ve already mentioned, there
are no fossil fuels, such as oil or coal, being burnt to produce energy. And so, there is no mass production
of greenhouse gases at a geothermal power station. Additionally, geothermal power
stations produce alternating current or AC because they use a generator to convert
the kinetic energy from the turbine into electrical energy. And this generator will produce
AC. This means that this energy can be
easily passed on to the transmission grid, which also uses alternating current.
So now, let’s look at some
disadvantages. One disadvantage is that geothermal
power stations can only be built in very specific locations. Generally, they need to be built
close to regions of volcanic activity where hot magma can be found relatively close
to the surface. Because in other regions, the rocks
closer to the surface of the Earth are much cooler, and the really hot rock is found
much deeper within the earth. Additionally, although running a
geothermal power station is not massively expensive, building one is. The initial investment required to
get a power station built and up and running is fairly large for the amount of power
that geothermal power stations actually produce.
So now that we’ve understood a bit
about geothermal power and seen some of its advantages and disadvantages, let’s take
a look at an example question.
The Geysers is the world’s
largest geothermal power station complex. It is located in the Mayacamas
Mountains, approximately 70 miles north of San Francisco. The installed capacity of the
power station complex is 1517 megawatts. Now, the first part of the
question asks us what is the total annual energy output of the Geysers power
station complex? Give your answer in gigawatt
hours to two significant figures.
Okay, so in this question, what
we’ve been told so far is that the Geysers is a geothermal power station
complex. And that power station complex
produces 1517 megawatts of power. We know that this is the case
because a megawatt is a unit of power. Based on this information,
we’ve been asked to find the total annual or yearly energy output of the Geysers
power station complex. So to do this, we need to
recall a relationship between the power produced by the power station complex,
the energy produced by the power station complex, and the amount of time for
which this energy is produced.
We can recall that power 𝑃 is
defined as the rate of energy transfer or the amount of energy in this case
produced by the power station complex divided by the time taken for that energy
to be produced. Now, in this case, we’ve been
given the power output of the power station complex. We know it’s 1517
megawatts. And we’re trying to work out
the energy produced in a time of one year. And so, we can start by writing
this information down. We can say that the power 𝑃 is
equal to 1517 megawatts and the time 𝑡 is equal to one year.
Now, to calculate the energy
output of the Geysers power station complex, we need to rearrange this equation
to solve for the energy output. To do this, we can multiply
both sides of the equation by the time 𝑡. Because this way, on the
right-hand side, we’ve got 𝑡 in the numerator and the denominator. These cancel. And so, what we’re left with is
that the amount of time for which the energy is produced multiplied by the power
output is equal to the energy output. However, remember, we’ve been
asked to find out energy output in gigawatt hours. So when we multiplied these two
quantities together of 1517 megawatts and one year, we’ll find the energy output
in megawatt years. And so, to find our answer in
the required unit of gigawatt hours, we should first convert our power into
gigawatts and our time into hours.
So let’s start by recalling
that one megawatt is equivalent to 10 to the power of six watts. That’s what the prefix mega
means. It means 10 to the power of six
or one million. And we can also recall that one
gigawatt is equivalent to 10 to the power of nine watts. That’s what the prefix giga
means, 10 to the power of nine. And so to convert from
megawatts to gigawatts, we can say that one gigawatt divided by one megawatt is
equal to 10 to the power of nine watts — that’s one gigawatt — divided by 10 to
the power of six watts — that’s one megawatt. So both on the left-hand side
and on the right-hand side, we’ve got one gigawatt divided by one megawatt.
At which point, we can see that
on the right-hand side, the unit of watts will cancel since we have it in the
numerator and the denominator. And the numerical value that’s
left is 10 to the power of nine divided by 10 to the power of six, which is the
same thing as 10 to the power of nine minus six, which ends up being 10 to the
power of three. And so, we find that one
gigawatt divided by one megawatt is equal to 10 to the power of three. We can then rearrange this
equation by multiplying both sides by one megawatt, which means that on the
left-hand side, we’ve got a megawatt in the numerator and denominator. And on the right-hand side,
we’re left with 10 to the power of three megawatts.
And so, our conversion factor
now tells us that one gigawatt is the same thing as 10 to the power of three
megawatts. Or equivalently, if we divide
both sides of the equation by 10 to the power of three, meaning it cancels on
the right-hand side, we find that one megawatt is the same thing as one divided
by 10 to the power of three gigawatts or one thousandth of a gigawatt, which
means that we can substitute the unit of megawatt here with one thousandth of a
gigawatt. And so, we find that the power
is equal to 1517 divided by 1000 gigawatts. This leaves us with 1.517
gigawatts.
And so, now that we’ve
converted the power into the required units, we need to convert the time into
hours. To do this, we can recall that
one year is equivalent to 365 days. And then, we can recall that
each day has 24 hours in it. So we can multiply our quantity
on the right-hand side 365 days by 24 hours per day because this whole fraction
24 hours divided by one day is the same thing as one, since 24 hours is the same
thing as a day. And so, we’re essentially just
multiplying 365 days by one. But by multiplying by this
fraction specifically, we see that the unit of days cancels since it’s in the
numerator and denominator. And our quantity then ends up
being one year is equal to 365 multiplied by 24 hours. This ends up being 8760 hours,
which means we finally converted both our quantities into the required
units.
And so now we can say that the
energy output of the Geysers power station complex is equal to the power output
of the Geysers power station complex multiplied by the time for which this
energy is being produced. In this case, we’re considering
the energy produced over a year. And now, we can substitute our
two quantities in. The power is 1.517 gigawatts
and the time is 8760 hours. When we multiply the two
quantities, notice what happens to our units. We’ll have a unit of gigawatts
multiplied by hours or gigawatt hours exactly as we’ve been asked to do in the
question. So multiplying the numerical
values together, we find that the energy output is equal to 13288.92 gigawatt
hours.
However, this is not our final
answer. Remember, we’ve been asked to
give our answer to two significant figures. So here is the first
significant figure and here is the second. To work out what happens to
this second significant figure, we need to look at the third significant
figure. The third significant figure is
a two. Now, two is less than five. And therefore, our second
significant figure will stay exactly as it is. And so, we find that to two
significant figures, the total annual energy output of the Geysers power station
complex is 13000 gigawatt hours.
Moving on to the next part of
the question then: In 2016, the total US electricity consumption was 4137
terawatt hours. What percent of this demand was
supplied by the Geysers? Give your answer to one decimal
place.
Okay, so in this question,
we’re being told that all of the energy consumed by the United States of America
in 2016 was 4137 terawatt hours. And we’re being asked to find
the percent of this total energy consumed that was supplied by the Geysers,
which we know to have produced an energy of 13000 gigawatt hours to two
significant figures. So, in other words, we’re being
asked to find the percent of 𝐸 subscript total, the total energy consumed. That is the energy supplied by
the Geysers, which we’ve called 𝐸. And to find this percentage, we
need to take the fraction 𝐸 divided by 𝐸 tot and multiply it by 100
percent.
Now, before we do this, there
are a couple of things we need to note. Firstly, we’ve got 𝐸 in
gigawatt hours and we’ve got 𝐸 subscript tot in terawatt hours. If we want to correctly find
the percentage of 𝐸 subscript tot, that is 𝐸, then we need to compare them
both using the same unit. So to do this, we either need
to convert 𝐸 into terawatt hours or we need to convert 𝐸 subscript tot into
gigawatt hours. Let’s do the latter. Let’s convert 𝐸 tot into
gigawatt hours.
To do this, we can first recall
that one terawatt is equivalent to 10 to the power of 12 watts. And as we’ve seen already, one
gigawatt is equivalent to 10 to the power of nine watts. So if we now divide one
terawatt by one gigawatt; that is, we divide the left-hand sides of the two
equations, then this is equivalent to dividing the right-hand side of the two
equations because simply one terawatt divided by one gigawatt is the same thing
as 10 to the power of 12 watts divided by 10 to the power of nine watts. On the right-hand side, the
unit of watts in the numerator and denominator cancels. And we’re left with 10 to the
power of 12 divided by 10 to the power of nine, which ends up being 10 to the
power of three.
If we then multiplied both
sides of the equation by one gigawatt because this way, on the left-hand side,
we’ve got a gigawatt in the numerator and denominator, this tells us that one
terawatt is equivalent to 10 to the power of three gigawatts. And so, we can substitute in 10
to the power of three gigawatts into our terawatt in the unit terawatt hours,
which leaves us with the total energy consumed by the US in 2016 as being equal
to 4137 times 10 to the power of three gigawatt hours, which ends up being the
same thing as 4137000 gigawatt hours.
And so, now, we can find the
fraction that we’re looking for 𝐸 divided by subscript tot multiplied by 100
percent. And so, with everything
substituted in, we find that this is equal to 13000 gigawatt hours divided by
4137000 gigawatt hours multiplied by 100 percent. We notice that we’ve got the
units of gigawatt hours in the numerator and denominator. And this simplifies everything
down so that the numerical value becomes 0.3142 dot, dot, dot percent. But we’ve been asked to give
our answer to one decimal place. So here’s our first decimal
place: it’s the three. Looking at the next decimal
place, we see that that is a one which is less than five. And therefore, our first
decimal place stays exactly as it is. It does not round up. And therefore, the answer to
our question is that about 0.3 percent to one decimal place of the electrical
energy consumed by the United States in 2016 was supplied by the Geysers power
station complex.
So now that we’ve had a look at an
example question, let’s summarise what we’ve talked about in this lesson. Firstly, we saw that radioactive
decay processes result in the heating of rocks deep within the Earth. In some parts of the Earth, such as
volcanic areas, this superheated rock, otherwise known as magma, can be found
relatively close to the surface. We also saw that water passing
close to this magma gets heated up. And this hot water can be brought
to the surface of the Earth, either by natural means or by pumping it up to the
surface. Then, the energy from this hot
water can be converted to electrical energy in a geothermal power plant.
Lastly, we saw some advantages and
disadvantages of geothermal power stations. Advantages include the fact that
geothermal power is a renewable energy source. Geothermal power stations produce
few pollutants once built. And they produce alternating
current, thus making it very easy to hook them up to the transmission grid. Disadvantages of geothermal power
stations include the fact that they can only be built in certain locations, areas
where hotter rocks are found closer to the surface of the Earth, such as areas of
high volcanic activity and the fact that geothermal power stations are expensive to
build.
