Study Guide

Fluids Themes

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  • Astrophysics

    Stellar evolution works like Hollywood. A star is born, burns brightly during multiple complex stages of life, and eventually runs out of fuel, becoming negligible because of brighter stars.

    Ultimately, what determines a star's fate is its initial mass. This is because the light we see from a star is a product of nuclear fusion inside a star, which emits tons of radiation, some of which we see as light.

    Fusing two nuclei together requires a huge amount of energy. Why? Well, nuclei have neutrons and protons. Neutrons are neutral but protons have a positive charge. As we know, positive charges repel each other, so getting them to fuse is a problem. A Hydrogen nucleus, for example, is a single, solitary proton. Fusing two of them means that they must have enough energy to collide into each other despite their like charges, and then one turns into a neutron, forming deuterium. Two deuterium nuclei colliding—again, only with sufficient energy—create a helium nucleus.

    Fusing hydrogen atoms can be done, but to do this, the core of the star has to reach very high temperatures, to the order of 5 million Kelvin. All this heat provides the necessary energy for fusion to occur. As it occurs, a star then exerts an outwards gas pressure. Since stars don't expand instantaneously, another force balances out this gas pressure. This other force is the star's own gravity based on its mass. The heavier the star, the stronger its gravity.

    Think of a cute little chickadee trying to hatch out of an egg. It tries to get out and explore the world, but the eggshell gets in the way. There is a bit of a struggle there for a while. Stars are like that.

    In this simplistic analogy, the eggshell is a star's gravity, and the chickadee provides the outward gas pressure. That means that until it goes super nova a star is in hydrostatic equilibrium, shown in the following diagram:

    For example, our Sun is currently fusing hydrogen into helium. When all hydrogen is consumed, the Sun will no longer have the ability to counteract gravity with gas pressure. Fear not, however; as it shrinks down a bit, it becomes denser, and its core heats up a little more. Soon enough, the temperature is high enough to start fusing helium. When that happens, then the star exerts pressure again, and reaches a new hydrostatic equilibrium.

    The star plays this game several times. Elements that end up being fused are, in order, hydrogen, helium, carbon, neon, oxygen, silicon and iron. How far the chain a star goes depends once again on its initial mass, since the initial mass determines what temperatures the core can reach. Small stars generally don't have enough mass to fuse elements heavier than oxygen.

    Larger stars, however, are massive enough to provide temperatures that can fuse elements all the way up to iron. Once a star has a core of iron, it can no longer resort to nuclear fusion to stay alive. This is because fusing iron together would require more energy than would be released, breaking a law of thermodynamics, but that's not our concern at the moment.

    Since iron cannot be fused, the star can no longer counteract its own gravitational pull with gas pressure. The star collapses upon itself, triggering the production of a supernova. This means all elements heavier than iron (including minerals that make up the human body) are and were created as a result of a star imploding into a supernova.

    Kinda cool, huh? We are children of supernova.

    Below is a summary of stellar evolution and the types of stars that can be created. Here, small stars are assumed to weigh less than 4 solar masses.

    Our Sun will eventually turn into a Red Giant, which will expand in size and gobble up Earth.

    Don't worry, though; this will only take place in a few billions of years, so we've got plenty of time to solve this problem. Maybe we can populate Mars or one of the moons of Jupiter, or leave the entire solar system by then.

  • Nuclear Physics

    The Liquid-Drop Model

    Who thought when starting this unit we'd be learning about nuclear physics? We didn't, so it's all good.

    We've learned that matter is made of atoms. Atoms are made of particles. What and where are those particles?

    The three principle particles of an atom are its orbiting electrons (with a negative charge), neutrons (guess what, they're neutral), and protons (protons are positive). Since they live in the nucleus, neutrons and protons are called nucleons. The nucleus needs a lot of energy to make sure it doesn't fall apart. We call this nuclear glue "binding energy."

    It doesn't quite happen like this, but for the sake of clarity, we like to think of the atom as a simplified solar system. The Sun is the nucleus, which is made up of nucleons, and the planets are identical electrons. Electrons orbit the nucleus.

    The nucleus is positively charged. How do we model that?

    Nuclear physicists have come up with two kinds of models, and both work: the shell model and the liquid-drop model. Since we are studying a module on fluids, let's stick with the liquid-drop model.

    The liquid drop model assumes a few basic things: a constant density, a size proportional to the number of nucleons, and a binding energy that varies depending on the mass of the nucleus, which makes sense. We'd need a larger nucleus to house more nucleons, and more nuclear glue if the nucleus is bigger. A constant density implies the effects of all the nucleons average out throughout the nucleus. Is this starting to sound familiar?

    Yep, sure is. This sounds exactly like a drop of water. And yes, we totally knew that.

    Just like a drop of water, the particles within a nucleus can also vibrate, rotate, and change shape as long as its volume is constant. A drop of water has a constant density and is larger with more molecules. Remember what heat of vaporization is? In a way, it's exactly like binding energy. We'd have to provide a drop of water a certain amount of heat to break it apart into gas.

    In the case of a nucleus, we'd have to do exactly the same but to break it apart, we'd have to conquer its binding energy. It doesn't matter how this energy is provided and in what form because energy is energy. All that matters here is that the amount needed to break apart the nucleus is equal to its binding energy.

    We weren't lying when we said fluids are everywhere. What's even cooler is that the way we deal with them can be applied to multiple topics in physics, even more than the ones we've talked about thus far.

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