Video: Geothermal Power

In this video, we will learn how to describe the advantages and disadvantages of geothermal power, and which locations are suitable for geothermal power stations.

15:07

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.

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