Clear Science!

A current (simplified) view of the electrical grid shows that the demand for electricity and the amount of electricity generated must essentially match. This is done by ramping power plants up and down as people change how much electricity they want.

Solar power and wind power are not easy to regulate. But we want to be able to make them a large part of the grid, since they’re green. One way to do this is add electrical storage to the grid, which is like being able to put electricity in a box and save it for later. During periods of low demand you fill up the storage and then use it during high demand. A charged battery is an example of “stored” electricity.

Humanity uses about 15 TW of power. (That’s 15,000,000,000,000 watts. TW means terawatt, which is a trillion watts.) By comparison 120,000 TW of sunlight falls on the Earth. Ideally, this means one hour of sunlight could power us for one year. Practically, the top end of what we could collect would be around 600 TW, which is still a huge number. In other words, solar power could solve a lot of problems.

Solar cells like those you have probably seen work by using sunlight to make electrons move in a circuit, which is electricity. The most common design is made of layers of n- and p-type semiconductors. Light separates an electron and a hole, and the semiconductor layers make them go different directions to recombine. You cleverly make the electron go through a circuit and you get electricity.

The challenges to widespread use of solar cells are cost and intermittency. This is a good problem for scientists and engineers.

We’re going to address the question of why making energy generation more environmentally sustainable is an important but difficult problem. Take solar power. One very big problem with solar power one may not realize is that it is intermittent and unpredictable.

Of course you know the sun shines in the daytime and goes down at night. If you plot power generated versus time of day, this will produce a smooth parabola (arc or rainbow shape). When clouds go over, however, it causes sudden dips. Your solar array might even shut off. 

You may wonder, even though the Fukushima reactors were immediately shut down during the Sendai earthquake, why are they having a possible meltdown several days later? The figure shown above is from the website AllThingsNuclear. This plot shows the gallons per minute of cooling water boiled by a reactor of the Fukushimi type as a function of time since shutdown.

Even after control rods are inserted and a reactor is shut down, neutrons will still be produced for some time in the fuel rods. Over time the reaction will slow down and stop, but it is not instant on/off. Engineers use fairly complicated mathematics called control systems to regulate things like this that have time lags between a control input (“turn off”) and a system response (it actually turning off).

Even a week after shutdown, the reactor needs to boil off 60 gallons of cooling water per minute to stay at a steady temperature. This is all planned for. The problem in Japan is that the fossil fuel generators meant to keep cooling water flowing in an emergency failed.

In light of the emergencies at the Fukushima I and II power plants in Japan, we’re going to talk about nuclear power plants for a while. Nuclear power is not super-complicated: there is nuclear fuel, for example either UOX or MOX pellets (uranium oxide or mixed uranium and plutonium oxides in this case), which are packed into zircaloy ceramic rods. The job of the rods is to get hot. This is just like in a fossil fuel power plant, when it’s the coal or oil’s job to get hot.

The fuel rods are surrounded by water, which gets hot, boils, and carries the heat away. In the picture above, the red line is the heat generation profile in the rods: they generate the most heat at their center. Think of the heat as a thing that is generated there, diffuses through the solid rod to the outside, transfers to the cooling water, and exits with the water as it boils and becomes steam.

If there is an interruption in this heat transfer path, then heat will begin to build up. Think of it as a heat traffic jam. If the heat begins to collect in one spot, the temperature there will rise. The zircaloy and nuclear fuel pellets are ceramics and have extremely high melting points. However, if you get a big enough heat traffic jam, they will eventually melt. That’s called a meltdown.

We’re going to talk about entropy for a while. You may have heard of entropy: it is often called a measure of the “disorder.” The second law of thermodynamics says that the entropy of an isolated system must increase with time. The universe is assumed to be an isolated system, and therefore the “disorder” of the universe is increasing.

When entropy was first discovered by Rudolf Clausius in 1865, the main application for such a finding wasn’t abstract, philosophical musing about the fate of the universe. Rather it was the question of machines and power generation by mankind, which are directly related to entropy in a practical way.

What if instead of defining out system as a tank with water flowing in and out (or a herd of cows), we choose the atmosphere of the Earth as our system, and consider the flow of carbon dioxide (CO2) in and out of it?

When people worry about CO2 going into the atmosphere, what they’re really worrying about is how long it will stay there, and how much it will build up. CO2 goes into the atmosphere anytime we burn something. However, the ways it can flow out of the atmosphere are more limited. It can:

• Dissolve in the ocean
• Get breathed in and incorporated by plants
• Get incorporated in rocks and minerals like limestone (CaCO3)

If the flow in is much bigger than the flow out, then the stock of CO2 in the atmosphere will not be steady, but will increase over time. Calculating CO2 residence time gets more difficult, but the smaller flow out is, the longer residence time becomes.

We talked about residence time of water in a tank, and we also gave an example of residence time of medicine in a patient’s body. The concept of a residence time can also be used in more abstract situations.

Say you have a herd of 42 cows, and the size is steady over the years. 7 cows are born each year. Now, since there are cows being born, and the herd is a stable size, that also means some cows are dying (poor cows), and at the same rate: 7 per year.

What’s the residence time of cows in the herd? F = M/T. Rearrange to get T = M/F. Plug in: T = (42 cows)/(7 cows/year). T is a residence time of 6 years for the cows in the herd.

PS the natural lifespan of a cow is 15-20 years. These cows were going to McDonald’s. (Eat mor chikin.)

We talked about residence time, giving a simple equation to find it: F = M/T, where F is the flow in and out, M is the stock, and T is the residence time. When using an equation like this, you need to pay attention to the units that go with the values you plug in.

Say the flow in is 5 gallons per minute (gal/min), and this is also equal to the flow out. The stock, or size of the tank, is 500 gallons. We easily plug in the numbers and find that the residence time T is 100.

But 100 what? The residence time is 100 minutes, and we know that by doing the same math we did on the numbers on the words that go with them.

Let’s talk about a basic concept of engineering: a residence time. Think of a tank. Liquid pours in, and liquid also empties out.

Suppose we say the liquid inside the tank is our system, which is highlighted in the lower picture. For the level in the tank to stay the same, the flow in (F in) and the flow out (F out) have to equal each other. We have a special name for the liquid inside the system at any given time, and that is the stock (M).

What if we want to know how long each water molecule spends in the tank? Well, the molecules might all spend different amounts of time in the tank. Suppose one molecule in particular takes the path of the dotted line. It might spend longer in the tank than a molecule that went straight from the inlet to the outlet.

Ok, but we can calculate an average amount of time each molecule spends in the tank, using the equation shown. This is the residence time, symbolized by T in the equation.

This isn’t used just for tanks and water. Imagine this: what if the tank is the blood in your patient’s body, F in is the flow of medicine into the patient by and IV, and F out is removal of the medicine from the blood by the kidneys. You can also calculate a residence time.