Unit (part 2)

CONTINUED from Unit (part 1)

The other thing about the Universe, besides spacetime, which we can easily relate to, has to be matter. No question about it. Again, it’s something we are all familiar with just by virtue that we are made of it! Matter has several characteristics. It takes up space, for example, and we’ve already addressed that above. It grows old and dies or it decays over time or maybe not; maybe it stays intact no matter how long you wait. So there’s this aspect of time as well – and we’ve talked about that. Matter also has this property we call mass. Mass, incidentally, is another one of those fundamental quantities. We often talk of the ‘mass’ of something as though it means ‘the amount of stuff‘ in it. That’s fine as long as we don’t mistake it for ‘the amount of substance‘. Strictly speaking, ‘mass’ and ‘amount of substance’ are two distinct fundamental quantities.

The cradle of stars © NASA

Before Einstein came along, the relationship between mass and energy was distinct. Mass pertained to the material aspect of a body while energy had to do with the intangible or the immaterial. But ever since Einstein showed that there is an unambiguous relationship between energy and mass, mass can also be associated with immaterial things, like radiation for example. In that sense, light from a candle flame has mass as does the candle itself. Einstein’s famous equation E = mc2 elegantly encapsulates this equivalence between energy and mass. But what exactly is this thing we call mass?

Well, there are two ways to go about answering that question. First, mass is that property of a physical entity (whether it is material or immaterial) which impedes its relative state of rest or motion. In other words, if something is comfortably at rest then, for it to start moving, it has to overcome something. That ‘something’ is what we call its inertia. And that which bestows the inertia, or resistance to motion, on that entity is what we call mass. More specifically, we call that ‘inertial mass’. Put simply, it’s the property of an entity that resists a change in motion. A second way to think of mass is in terms of the force of gravity. If something has this property which makes it react to the force of gravity then it has mass. In this case, we call it ‘gravitational mass’. It is akin to the magnetic property of some metal, for example. A paper clip has this property which makes it stick to a magnet. It reacts to that force, that magnetic force, exerted by the magnet and is pulled towards it. The paper clip is therefore said to possess this property we call magnetism. Likewise, when the very same paper clip is dropped, it falls to the ground. It reacts to the force of gravity exerted by the Earth and is pulled towards it. The paper clip is therefore said to possess this property we call mass. So far, so good. But that is not the end of it. Cue in Einstein once again. In his seminal paper, The General Theory of Relativity, he showed that inertial mass and gravitational mass are equivalent. So this property which makes a body resist motion is the same one which makes it react to the force of gravity. Einstein referred to this as the Equivalence Principle.

Now that we know what mass is, how do we quantify it, how do we measure it? The SI unit for mass is the ‘kilogram’. The rather special case of this unit is that it is directly related to an artifact. Unlike the units for time and length, which depends on some physical property that can be replicated anywhere (the vibrations of the caesium atom and the distance traveled by light), the kilogram is defined by this cylindrical block of platinum-iridium alloy stowed away at the International Bureau of Weights and Measures. The trouble with this is that the metal block is subject to even the tiniest of alterations over time causing its mass to change even by the most infinitesimal amount. And this is unacceptable. Our reference points have to be reliable, accurate, reproducible and invariant. As such, physicists are still debating over how to find the correct reference for the kilogram. One which is related to an unwavering fundamental constant of nature. As yet there is no consensus on what that constant should be; so until further notice, we’ll have to use that metallic alloy in France.

Still on the subject of matter, there are other material properties which allow us to define the fundamental quantities. Mass can relate to either a material or immaterial entity. But if we restrict our scope to material entities only then we can define another fundamental quantity called ‘the amount of substance‘. All of matter is made up of particles, be they molecules or atoms. Now molecules and atoms are so tiny that we need a huge amount of them to form even the smallest amount of stuff. For instance, a drop of water might contain about a thousand billion billion molecules! This is an approximation but, even then, we can see that there are quite a few molecules in a single drop of water. Likewise, if we take a certain amount of carbon we can figure out the number of atoms it’s made up of. One thing we need to note here is that there are different kinds of carbon atoms. The difference is subtle yet crucial. Some carbon atoms are slightly more massive than others. Thus, we need to specify which particular type of carbon we are looking at prior to counting the number of atoms it is made up of. Those variants of the carbon atoms are called isotopes. In our case, we’ll be looking at the carbon-12 isotope. There’s also the carbon-14 isotope which is related to the carbon-dating method of determining the age of fossils.

In exactly 12 grams of the carbon-12 isotope, there are 6.02214179×10^23 atoms. This is about 600 thousand billion billion atoms in only 12 grams of carbon-12! Numbers too large for us to grasp but important nevertheless to be aware of. That number is a special one for it underlies the definition of the amount of substance. The amount of substance of a given entity is the number of particles it is made up of compared to the number of atoms in 12 g of carbon-12. So this fundamental quantity is like a ratio. It compares one characteristic of something to a similar characteristic of a reference point. Here, the reference point is 12 g of carbon-12 and the characteristic in question is the number of particles being counted. So what this gives us is a way to quantify amounts of substances. For example, how much oxygen do I need so that there are the same number of oxygen atoms in that sample as there are atoms in 12 g of carbon-12? Or, if there are a trillion atoms of hydrogen in a given sample, then what amount of hydrogen does the sample contain? That quantity is the amount of substance and its measured in mole. One mole of carbon-12 has 6.02214179×10^23 atoms and has a mass of 12 g. One mole of hydrogen-1 isotope has 6.02214179×10^23 atoms and has a mass of about 1.008 g. The mole comes in handy when dealing with chemical reactions. Instead of talking in terms of grams of atoms, we talk in terms of moles. It’s just easier to manipulate the figures when expressed in moles. Mix 2 moles of hydrogen atoms with 1 mole of oxygen atoms and there you have it: 2 moles of water.

Another characteristics of matter is its temperature. That’s another aspect with which we are all very familiar with. As seasons change we notice the varying ambient temperature. When we’re feverish our body temperature is elevated even if we’re shivering under the blanket. Holding a nice warm mug of hot chocolate is comforting during the cold winters while there’s nothing more refreshing than nice cold beer during a hot summer. If you want to learn more about temperature itself please see my blog called Thermal. In short, however, temperature is a measure of internal energy of a system. This is a very basic definition but it will suffice for now. Remember that all of matter is composed of molecules or atoms. Each of these particles are in constant motion, jiggling about, whizzing about as though they’re nervous and restless. The moving particles possess a type of energy we associate with motion. This energy is called kinetic energy. The particles also have a tendency to attract each other; they pull on each other as much as they can unless there is some external agent trying to force them apart. This mutual attraction relates to another kind of energy we call potential energy. The combination of the kinetic and potential energies of the constituent particles is what gives rise to the internal energy of the system. And temperature is just a way to quantify that energy. The more energy a system has, the hotter it is. The converse also is true. The lower the temperature, the less energy it has.

Most people refer to temperature in terms of degrees Celsius and some (those who haven’t adopted the metric system yet – I’m not going to name names but the USofA knows who I’m talking about) still use Fahrenheit. But neither of them are the standard units for temperature. Temperature in SI units is measured in kelvin and its symbol is K. And so, on a nice warm day it might be 27 degrees Celsius – this would be equal to 300.15 K. A freezing 0 degree Celsius is exactly 273.15 K. 0 K, however, is the lowest ever temperature there can be. There is nothing, absolutely nothing, colder than 0 K. It’s not that we haven’t yet observed anything colder than 0 K. It’s really the lowest of the low. It’s limit is a mathematical definition and is the point where the internal energy of a system reaches 0. Since there cannot be anything with less than zero energy, the temperature of a system cannot fall lower than 0 K. On the other hand, the is no upper limit to how high temperature can get. The surface temperature of the Sun is about 5 800 K, for instance, while its core is a whopping 15 million K!

Speaking of the Sun, there is another characteristic of matter which has to do with the amount of light it emits. This particular property is called luminous intensity. Not every body emits light but for those that do, it is a fundamental quantity. It is a measure of how much light is being emitted from the source in a given direction. It’s unit is the candela and is represented by the symbol cd. Luminous intensity is not a widespread quantity which we are likely to come across. Unlike mass or time, luminous intensity is associated with a very limited set of entities. Yet, it is a fundamental quantity upon which other light-related quantities are derived.

One last characteristic which is related to matter is the electric current. Again, this is a property we are all very familiar with. A world without electricity would take us back to the Dark Ages. I’ve given a short explanation on what electricity is in my blog called Electricity. Put simply, electric current is the rate of flow of electric charge. What that means is that, inside conductors such as copper wires, there are swaths of electrons which are shaking about transferring this thing we call electricity. How much of these electrons (the electric charge carriers) are going past a certain point in the wire is what determines the current. Larger current implies more electrons are going past in a given time. Good conductors, therefore, have many more electrons available compared to insulators. This is the reason why conductors can allow more charges to flow per unit time and thus allow more current to pass through them. It’s as simple as that really. Current is measured in Ampere and is often quoted on the electrical fuse. One with 13 A on it implies that it can sustain a maximum current of 13 Ampere. If current larger than 13 A were to flow through the fuse, it will blow.

So there you have it. There are 7 fundamental quantities and these are: time, length, mass, amount of substance, temperature, luminous intensity and electric current. The reason they are fundamental is because all the other physical quantities, such as force, volume or electric charge, are all derived from these magnificent seven. It is crucial, therefore, to ensure that their definitions are accurate and reliable. These quantities are to do with everyday things, for most part, and are relevant to our daily lives. We cannot underestimate the importance of that list and this is the reason why we learn about them as part of the very first lesson in Physics. In fact, more than just a list of quantities to remember, these fundamental quantities are the pillars of foundations on which the edifice of Physics stands tall.

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One thought on “Unit (part 2)

  1. Pingback: Unit (part 1) « electrolights

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