Wednesday, November 21, 2012

10 interesting facts I have learned from Physics

This post I will write about my favorite facts I have learned about Physics over my 4+ years of study.  I still have much to learn, but as of now these things really hit home with me.  They are in no particular order.  I want to make this post really "lamen." Meaning I made sure to keep math out of it.  I also excluded a lot of topics in physics that would require too much explanation   For example, Quantum Mechanics has many interesting things about it, but its concepts are so strange, many people wouldn't appreciate it.

What makes things solid? We don't actually "touch" anything!:

We all know what it is like to feel things, particularly solid objects. We touch them with our hands, or walk on them with our feet, and every time we get the same response, an equal an opposite force backwards, the object "feels" solid.

But what is going on there? If we zoom in extremely close between the atoms in our fingers or feet or what ever to the object we are touching we will notice something interesting.  As you probably know all atoms are made of a nucleus composed of protons and neutrons and are surrounded by a cloud of electrons. Solid objects are a neat array of these atoms called a lattice.  

When we go to touch anything, or walk on something, the outer electrons in the atoms in our hands or feet repel the outer electrons in the solid object. So technically nothing actually "touches" There is always a measurable distance between the atoms in our hand and in the table or floor or cat.  So "touch" is nothing more than the electrostatic repulsion between atoms!

To put this in perspective, this is the same force that makes water from the kitchen sink repel a freshly used comb. It also can be used to show just how weak the gravitational force is.  The entire weight of your body is being held up by the repulsion of the atoms in your feet.

So technically, when you are sitting in your chair, you are actually floating slightly above it, since the atoms in your butt can never "touch" the atoms in the chair.

How do Air-Conditioners make cold air?

For this one I need to first set up a scenario. Imagine you have a pan of water.  You put this water in an oven until it starts to boil.  As soon as it starts to boil you immediately turn the over up to 2 million degrees. Neglecting the fact that the pan itself would melt (imagine we have some super, indestructible pan), the water would still continue to boil, albeit much quicker, but it would still boil.  The question is, what is the temperature of the water while it is boiling?

Well water boils at 100 degrees Celsius and interestingly enough, this will be the temperature of the water! Even if the oven is 2 million degrees.  All the energy is going into transforming the liquid water into a gas and none of it goes into actually making the temperature of the water hotter.  So the water will stay 100 degrees no matter what the ambient temperature is.  The only way the water can increase temperature is when it ALL turns into a gas.

It doesn't have to be this way however, if we wanted the water to boil at a much higher temperature, we would simply increase the pressure in the oven.  This works because the air molecules are colliding with the water much more frequently and thereby causing them to stay together in a liquid state and not fly off into a gas.  So we have learned two things here.

1. When a substance starts to boil, it continues to stay at its boiling temperature no matter how high the ambient temperature is.  It continues to do this until all the substance turns into a gas.

2. Increasing the pressure increases the boiling point of a substance. And decreasing the pressure decreases the boiling point.

So what does this have to do with air-conditioning?  Well it works on the same principle! Without going into detail about how EXACTLY it works, here is the general idea.

Instead of using water, we will use a different substance.  We will use a substance called a refrigerant, people know this as "Freon" but this is not correct since "Freon" is the name of a company that makes the refrigerant.  The most common type of refrigerant is called R-134a.

So what makes something a refrigerant?  The fact that its boiling point is extremely low (as well as having many other properties).  R-134a has a boiling point of -15.7 degrees Fahrenheit, meaning it would be a gas under normal atmospheric conditions.

An air conditioner pressurizes R-134a to a very high pressure. As we learned, this will raise the boiling point.    It can be raised so much that above room temperature it is in a liquid state.  The air-conditioner then rapidly drops the pressure, this consequently causes the boiling point to go back to -15.7 F.  But remember, when something is boiling, it STAYS at its boiling temperature no matter how hot the outside is.  So all the refrigerant suddenly becomes -15.7F.  This rapid cooling of the refrigerant causes the air around the refrigerant to be cooled considerably by convection, and a fan then blows this air out.  This is the cold air we feel!

Time can travel slower for some than others:

A lot of my favorite things come from Einstein, and this is one of them.  Among other things, Einstein discovered that time is not constant. (He called it "Time Dilation")  Meaning that it is possible for time to travel slower for some than others. But what is the factor that determines how fast or slow time travels?

The answer to that is speed.  The closer an object travels to the speed of light, the slower time travels.  Interesting scenarios can be made from this fact.  For example, the "Twin Paradox" is one such famous example.  If you took two twins, and put one in a rocket ship that traveled at 99% the speed of light and let the other stay on earth, then in 70 years the twin in the rocket ship would only be about 10 years older! So you would have two twins, one 60 years older than the other!  Time travels roughly 7 times slower for the twin in the rocket ship.

One interesting fact about this is, we need to use Einsteins corrections in satellites orbiting earth.  While these satellites are no where near even 1% the speed of light (about 11.2 kilometers per second), there is still a small amount of time dilation and this small error would be enough to make our GPS devices not work correctly on Earth.


Electricity travels quite slowly:

Any Physicist would look at this title and be confused as to what exactly I mean by "electricity." It is a very broad term.  Because certain aspects of electricity travel quite fast, for example when you flip the light switch, the light turns on immediately, what is traveling slow there? Seems pretty fast right? Well you are "kind of" correct.

When any circuit is completed, (as in flipping a light switch) an electric field is generated.  This electric field originates from the voltage source the circuit is powered by, be it a battery or an outlet in the wall. (Doesn't matter if it is AC or DC.)  This electric field pushes the electrons in the wires and this creates the flow of electricity. Electricity is nothing more than the movement of electrons.

So what moves slow? Well when you flip the switch, the electric field propagates extremely quickly.  In fact, the electric field generation and propagation is close to the speed of light.  But remember this field pushes electrons, and the flow of electrons is what electricity is.  The problem is, while the electrons are moving, the atoms in the wire get in the way.  This consequently causes the electrons to collide with the atoms and get redirected, many times even in the opposite direction! But since the electric field is always pushing forward, their average movement is forward.  But because of all these backward collisions, the average rate the electrons move is actually EXTREMELY slow.  On the order of a couple centimeters per second.  The reason why, say a light bulb, illuminates very quickly is because there is already atoms in the filament of the bulb and the electric field causes them to move.  It is the local movement of the electrons in the filament that causes the light bulb to illuminate. Depending how long the wire is from the power source to the bulb it could take over an hour or more for the electrons to go from the power source to the light bulb!


Getting shocked by a door knob and by lightning are the same thing:

We have all been shocked before.  Whether it is by a new sweater or a door knob.  The interesting thing is that the same physical laws that cause this shock are the same laws that cause lightning.  

When we get shocked by a door knob or anything else in daily life, it is because some time in the day we build up charge from rubbing and sliding on different substances.  So our body now has an accumulation of charge.  When we touch something metal that has also been rubbed on, the metal object has a deficit of charge, while you have a abundance.  When you get close to the object the extra charge will "jump" through the air and onto the metal object, restoring both you and the object to a neutral charge state. Interestingly, this shock will be a few thousand volts!

Lightning works the same way.  Somehow (it is still not fully understood) charge builds up in the clouds. Scientists believe it has something to do with raising water droplets in the atmosphere and somehow this builds a charge.  Never-the-less, a charge is built up in the clouds.  Which means there is a charge difference between the ground and the clouds.  If this difference becomes high enough the charge will "jump" from the clouds to the ground, restoring both to a neutral state.  The only difference is that this is a MUCH MUCH higher scale than the door knob and will be likely to kill you.


Visible Light, Radio Waves, Gamma Rays, X rays, All the same thing!:

James Clerk Maxwell, with the help of Michael Faraday discovered that light is an electromagnetic wave.  An electromagnetic wave is a wave composed of oscillating electric and magnetic fields.  This is how they work.

Through the laws of electromagnetism, we have learned the following.
1. A changing electric field generates a magnetic field.
2. A changing magnetic field generates an electric field.

An electromagnetic wave is made when either an electric field or magnetic field is created. As the field is being created it is "changing" and thus, according to the laws above, will generate the opposite field.  So if we generate an electric field, it will immediately start generating a magnetic field.  But then this new magnetic field will start generating another electric field.  This continues indefinitely and creates a propagating wave through space called an electromagnetic wave.  This is what light is.  Here is an animation from Wikipedia of the process. (Really cool!) (Click the image to make it load faster.)
One color is the electric field and the other color is the magnetic field. (Wildly out of scale!)  Notice that they are perpendicular to each other.

This is light. But it is also radio waves, and X-rays and gamma rays and microwaves. In fact, all these are exactly the same thing! So why is visible light safe for us while gamma rays are deadly? It is because of the energy the wave carries.

Without going into the math, the energy in an electromagnetic wave is directly proportional to the wavelength of the wave.  Small wavelengths correspond to HIGH energy and low wavelengths correspond to LOW energies.  The only difference between light and gamma/microwaves/X-rays/etc is the wavelength of the wave. That is IT! 

How do Microwaves cook food? Are they radioactive / dangerous?

I see / hear it all the time.  People VASTLY misunderstand microwave ovens.  Many people will downright think these things are radioactive and dangerous.  How do these things magically cook our food while not heating anything up?

Well above we learned that microwaves (not the oven! The wave!) are an electromagnetic wave.  We also learned that the only difference between light and other forms of electromagnetic waves is the energy they carry (which translates into a different wavelength).  Here is the interesting part, microwaves have LESS energy than visible light! Meaning the light around you is more "powerful" than the microwaves in the microwave.  

A logical question might be, "Well if they are so weak, how do they make my food so hot?!"  Good question! It has to deal with the fact that they interact with water molecules.  All food contains water in it.  Water is known as a "polar molecule" which means it is not electrically neutral.  It has a positive side and a negative side.  When something is of this form, it is called an "Electric Dipole," or said to have a "Dipole Moment."  Since the electromagnetic wave contains an electric field, it interacts with the dipole moment of the water molecule and causes it to oscillate.  Any electromagnetic wave will do this to water but there is something special about a microwave...

Every object has a "resonance frequency" in which if you oscillate the object at that frequency it will shake so violently that eventually it might cause some major problems. Soldiers marching over a bridge have been known to collapse it because they were marching to the resonance frequency of the bridge.  This also has happened on bleachers of people tapping to the rhythm of a song playing.  The rhythm just so happens to be the resonance frequency of the bleachers.  Water also has a resonance frequency.  This frequency is exactly the frequency of a microwave.  So the reason why microwaves cook food and not light or another EM wave is because the microwave is at the "special" frequency that causes the water molecule to oscillate very violently.  This oscillation causes inter-molecular "friction" and this friction causes heat. (Just like the friction in rubbing your hands together causes them to get hot.)  This heat by the friction causes the food to cook.

This is why the parts of the plate that aren't touching food stay the same temperature and why the microwave itself does not get hot.  So it is not because microwaves are powerful or "radioactive" that causes them to cook food.  They simply are just at the "right" frequency to oscillate the water molecules in the food.

How do Motorcycles stay stable?

A common toy you can buy is a "gyroscope."  It is also a very interesting topic in Physics.  A gyroscope is caused by a rotating wheel about an axis.  Here is a picture of a toy gyroscope.
Anyone who has ever played with one of these will know it can have some very strange behavior.  While the wheel is spinning, the gyroscope will stay stable (as shown in the picture).  If you try to tip it over it will cause the gyroscope to turn and move in a surprising manner. The mathematics behind this are a little on the complicated side but it has to do with the fact that angular momentum is being conserved (not important for this article!)

The wheels of a motorcycle about their respective axis act as gyroscopes.  While the wheels are spinning it increases its angular momentum.  If you try to tip the motorcycle over, the torque you exert on the motorcycle will be translated into a turning motion.  This is why motorcyclists lean to make turns.

This is a very complicated situation to describe without the help of mathematics, but if you go buy one of these toys (they are like 2 bucks!) you can get a big understanding on how gyroscopes work.  They work based on the fact that the wheel is turning.  If the wheel starts to tip over, the rotating mass of the wheel "throws" it back upright.

The strange properties of gyroscopes also make motorcyclists employ the use of "counter-steering" in which, over a certain speed (about 10mph) they need to turn their handle bars the OPPOSITE direction of their turn.  For example, they would turn the handle bars left, to go right.

What Causes Magnetism? How are magnets made?

Everyone knows what a magnet is. We all know that opposite poles attract each other and similar pole repel each other.  Here are some questions..
1. What causes a magnet to have such properties?
2. What happens if you cut a magnet down the middle between the two poles?
3. Do we actually know WHY magnetic fields exist?

1. So let's answer the first one. What causes, say a fridge magnet to stick to certain types of metal?  To get the answer we need to go on an atomic scale and look at the electron.  Electrons have a certain property called "Spin" which emulates the spinning of charge. Due to the laws of electromagnetism, a moving charge crates a magnetic field.  So the "spin" of the electron causes it to create a little magnetic field.  Also known as a Magnetic dipole. If the spin is in one direction is creates a +- dipole and if it is in the other direction it creates a -+ dipole. (The "spin" of an electron isn't actually the electron spinning, it is actually a little more complicated than that, but for now, this interpretation works.)  In a material like metal (or any other material for that manner) all the magnetic dipoles from the electrons are all randomly oriented.  Therefore the average magnetic field when adding up all of them is zero.  In certain metals, the electrons in the outer shell of the atom are not bound like they are in, say wood.  So when a magnetic field is applied to them it re-orients the dipoles to all be in alignment.  The sum of all these dipoles creates a macroscopic magnetic field that we can feel when we play around with magnets.  When we go to stick these magnets on the fridge, the magnetic field turns all the magnetic dipoles in the metal in the fridge to be in the opposite direction of the ones in the magnet and thus creates an attraction.

This is how we make magnets.  Certain materials (ferromagnetic materials) retain the orientation of the magnetic dipoles more strongly than others.  So it is possible to magnetize these substances by simply applying an external magnetic field.  Interestingly enough, you can also reverse the process by adding heat.  This causes the atoms in the material to oscillate violently and re-randomize the magnetic dipoles.

2. This is very interesting.  When you cut a magnet down the middle of its poles, it will create two smaller magnets with two poles.  It is impossible to have one magnetic pole isolated, they ALWAYS come in pairs.

3. The simply question of "Why do magnetic fields exist?" to this day is still not answered. We know HOW they work in incredible detail, but we still do not know WHY!

What is Gravity?

I saved this one for last because it is the most complicated.  It again is from our good friend Einstein.  When Newton formulated his equations and laws of gravity he himself said that he has no idea what gravity is or why it exists, but he can explain how it works.  Einstein answered this question.

The following ideas are very complex and require a very extensive imagination to visualize.  Einstein states that space and time are not two separate concepts but rather, interwoven together to form a four dimensional "space-time."  Where three dimensions come from our world we live in and the fourth dimension is time.  Think about it, if I say "Ill meet you in the parking lot."  I gave you a place, but not a time, you need more information.  Conversely, if I say "Ill meet you at 5:00 PM."  Again, not enough information, I gave you a time but not a place.  Therefore it only makes sense that in order to describe something completely we need both a spacial component ( 3 dimensions) and a temporal (or time) component. (Adding an extra dimension.)  When any mass is in this "space-time" it causes it to warp and bend, altering the paths objects take from straight lines to curved ones.  The earth travels around the sun because the space-time "fabric" is being bend and earth is simply stuck in it and follows the bent space time.

Since space and time are linked together, if space can bend, so can time.  The rate of time slows down the higher the gravitational force you are in.  This means time travels slower on the sun than on Earth because the sun has much more gravity.  The reason why a ball falls to the ground is because the space the ball is traveling in is being curved downward and the ball is simply following this curvature.



Wednesday, November 14, 2012

Deriving Boltzmann's Constant

This is one of those really simple things that is still really cool to learn.
Starting from the ideal gas law..
Where P is the pressure, V is the volume, n is the number of kilomoles there are, R is the gas constant and T is the temperature.

We will first start by dividing by Avogadro's number and assume we have one kilo-mole of gas. (Meaning n=1)

So the energy per-unit molecule is E=kT.