Alright, I'm going to teach you all thermodynamics.

[Red]

Because it will help me study for my test tomorrow.

OKAY, CLASS. Be excited. We're going to learn the processes involved when dealing with the Laws of Thermodynamics.

First, let me just explain something about hot and cold objects. In a closed environment, if you place a hot object and a cold object next to one another, energy (in this case, heat) flows between the two until the reach what is known as thermal equillibrium. This means that the the two objects will share the same temperature.

The Zeroth Law of Thermodynamics (silly, I know, and it's also kind of obvious) states that if one object (A) is in thermal equilibrium with another object (B), and that object (B) is in thermal equilibrium with another object (C), then the first object (A) is in thermal equilibrium with the last object (C). Trivial, I know, but very important.

Alright, now let's talk about thermal expansion. We all know that when an object is heated, like metal for instance, it expands, right? Yeah! So, first, let's talk about linear expansion, which only deals with one dimension.

Say that an object has a length of L0 to begin with. Add heat, and now we're at a new length of L. How'd we get there!?!?!? Well, simply put, because we know that the change in length is directly proportional to the material, the added heat, and the original length, we can say:

The change in length (delta L) = (alpha [coefficient of linear expansion, depends on the material])(L0, the initial length)(change in temperature).

L change = (alpha)(L0)(T change).

If we rewrite L change as L - L0, we can solve and get that the new length,

L = L0(1 + [alpha][T change]).

Because we figured that out, we can assume (because of the properties of area and volume), that surface expansion is based on the equation,

A change = 2(alpha)(A0)(T change)

and the volumetric expansion is based upon

V change = 3(alpha)(V0)(V change).

WHOOOOOOOOOOOP. We just learned expansion guys!

Now to move onto the MANOSCOPIC DESCRIPTION OF AN IDEAL GAS!!! or, as many of you may know if you are in chemistry or physics,

PV = nRT.

What's that, you say?

Well, this is just saying that if you are given a situation that you have an ideal gas and have to figure out something, you could use this equation where

P = pressure (in pascals)
V = volume (meters^3)
n = the number of moles of the gas
R = the constant, 8.31
and T = the temperature of the ideal gas (in Kelvin).

So, if you're given 4 out of 5 of these (or if you can figure 4 of them out in other ways), you can use this equation to solve for the 5th.

Some important things to know about ideal gases:

One VERY important equation to know is

(P0 x V0)\(T0) = (P x V)\(T).

Again, WHAT?

All this is saying is that in a gas, the pressure times the volume, over the temperature, will always remain the same. Meaning,

if the temperature is constant, P0V0 = PV (pressure is inversely proportional to volume)

if the pressure is constant, V0/T0 = V/T (volume is directly proportional to temperature)

and if the volume is constant, P0/T0 = P/T (pressure is also directly proportional to volume).

Using these equations, you can figure out some missing parts from the Ideal Gas equation and use it to solve.

Now, let's move on the the Kinetic Theory of Gases.

This theory makes 5 assumptions based on ideal gases.

1.) The number of molecules of an ideal gas is LARGE, and the distance between molecules is also LARGE compared to their incredibly small size.

2.) The particles all obey Newton's Laws of Motion. They also move RANDOMLY.

3.) The particles only interact through short range forces in elastic collisions.**

4.) The collisions with the walls of the container are also elastic.** (**note, in an elastic collision, no kinetic energy is lost)

and 5.) All molecules are identical.

Okay, those being said, we can use a lot math to derive the formula for the average kinetic energy of the particles of an ideal gas. We could do that, but let's not to save time and let me just tell you that

KEavg = (3\2) x Kb x T

where Kb = Boltzmann's constant, which is simply the constant from our ideal gas law equation (8.31) divided by Avagadro's number (6.02 x 10^-23) to get a value of about 1.38 x 10^-23, and T is the temperature of the gas.

Now, we can also say that the average kinetic energy of the particles = (1/2)mv^2, where m is the mass and v is the velocity now. Therefore, we can say that that is equal to (3/2)KbT, and if we solve for v, we get

v = sqrt(3KbT/m).

This velocity is called the root mean square velocity. If we were to graph the velocities of the particles of a gas on a graph, we would see that the v(rms) is pretty close to the most probable speed of any particle in the gas.

ANNNYYWAAAAAAAAAAAAAYYYYSSSS we can also say that the internal energy, u, is equal to the kinetic energy of ALL the particles, so we just multiply the whole equation for KEavg by N, the number of particles, and when we eliminate/solve we get that

u = (3/2)nRT, where nRT are the same from the Ideal Gas Law equation.

Okay I'd go into internal energy more with specific heat and latent heat and then finding work from a graph and then all that fun stuff but I am just too tired so we'll stop there today and probably never go back. Just wanted to try to type some stuff out to get it stuck in my head. None of you will probably read all of this but that's okay. Just a physics lesson for me moreso than you. KBYE

[Wooster]

What's the difference between the average speed of a gas and the root mean square speed?

Also, what is a microcanonical ensemble?

[Wooster]

Oh Oh, what is the mean free path of a gas molecule at temperature T? And what is the probability there will be at most one collision through a distance, d ,through that gas?

Also, who the hell is Helmholtz?? And why the hell does he get an A??????? As far as I am concerned there is only one A#1 >_>

[NINE-TAILS-BIJU]

i read all of it... well this is interesting since i know what i'm going to learn in a couple of years:-). coolio. oh yeah when i was reading the part about the "V Change" after that you made this ---"= 3" in the middle of that. it was funny. well thank you for filling my brain with interesting facts.

[Red]

Originally Posted by Wooster

What's the difference between the average speed of a gas and the root mean square speed?

Also, what is a microcanonical ensemble?

Isn't like the average speed the most probable speed? I don't know lol

I DON'T KNOW THIS ISN'T ON THE TEST

Originally Posted by Wooster

Oh Oh, what is the mean free path of a gas molecule at temperature T? And what is the probability there will be at most one collision through a distance, d ,through that gas?

Also, who the hell is Helmholtz?? And why the hell does he get an A??????? As far as I am concerned there is only one A#1 >_>

AGAIN NOT ON THE TEST D:<

NONE OF IT, REBEL, I SAY!


Also, @NTB, enjoy. Physics will be the worst year of your life, especially if you're going into AP.

[Wooster]

Originally Posted by Red

Isn't like the average speed the most probable speed? I don't know lol

I DON'T KNOW THIS ISN'T ON THE TEST



AGAIN NOT ON THE TEST D:<

NONE OF IT, REBEL, I SAY!


Also, @NTB, enjoy. Physics will be the worst year of your life, especially if you're going into AP.

You are no longer welcome in the fraternity of the scientist.

[NINE-TAILS-BIJU]

what's "AP", pretty sure it might be like 100x worse than it is now at school:-)

[Vex]

*one leg up on chalkboard*

*twerk and tell time bitches*

["The Batman"]

Witchcraft. All of it.