Clear Science!

If you Clear Scientists want to hear about standing waves and...

Thu, 13 Jun 2013 09:48:00 -0400

If you Clear Scientists want to hear about standing waves and harmonics, how about checking out our series on:

(It doesn’t have to do with harmonics, but we also explain how an electric guitar works even though you don’t ever plug it into an outlet. Electric guitars actually make their own electricity when you strum them.)

We talked about how integrals will tell you the “area...

Wed, 05 Jun 2013 13:55:36 -0400

We talked about how integrals will tell you the “area under a curve.” Look up above where we drew a trapezoid to find the area under the curve. A little bit of the trapezoid is actually over the curve though, so it’s not exactly the right area. But it’s close. If we want to get closer, why not use two trapezoids? Then we can add their areas together. Great, how about four trapezoids? Even better, but still a little bit off because the top of a trapezoid is straight, and the curve is curved.

With an integral it’s like you make the trapezoid width Δx infinitesimally small, in which case it becomes dx. Then you add up an infinite amount of them, so you’ve used the smallest trapezoid size possible. This gives you the true area under the curve.

When we were worried about a heat transfer problem, we spent a...

Tue, 04 Jun 2013 11:01:00 -0400

When we were worried about a heat transfer problem, we spent a couple posts on derivatives and what they tell you. Integration is the inverse of differentiation. If you do calculus you end up doing those two things over and over again: taking the derivative and taking the integral.

Up above we have a curve plotted, which is y = 1/x. (By the way, if you ever want to know what a curve looks like, try fooplot. Type in 1/x there and hit enter and you’ll see it.)

Note the shaded area we’ve drawn, which is the area under the curve between x = 0.5 and x = 2. If you want to know the area (A) of that, you multiply the curve by dx and integrate from 0.5 to 2. So basically integrals tell you area.

Okay, so let’s think about that. What is dx again?

Hey! Can you make a post for integrals like you did for derivatives? It was very helpful! And any other calculus topics as well would be MUCH appreciated. Thank you!

Tue, 04 Jun 2013 10:46:58 -0400

Of course we can! Coming right up.

(By the way username: under-lock-and-keyy we like your avatar because the Clear Science Staff are into heavy metals.)

From the Clear Science mailbag: I live in the lower part of...

Fri, 31 May 2013 14:44:44 -0400

From the Clear Science mailbag:

I live in the lower part of Michigan and I found a white metallic frog eating ants on top of my mother’s pepper plant. Do you know of a way that would help me identify it? I’ll attach the photos I took just in case you recognize it.

Why not, who doesn’t like frogs? The Clear Science Staff doesn’t know much about frogs, except this: When we see one we always pick it up, and it always pees on us. You think we’d learn.

Have a great weekend, Clear Scientists.

Trying to find the temperature decay from a flame, we came up...

Thu, 30 May 2013 11:57:00 -0400

Trying to find the temperature decay from a flame, we came up with two equations:

a heat flux balance, which we derived
Fourier’s law, which we said was more or less a fundamental law

Now, we combine them to get a differential equation (step 1). Step by step we work through eliminating the derivatives with integration. At the end we get an answer with two constants C1 and C2 in it (step 7). This always happens solving differential equations because each integration produces a constant. Then we take the boundary conditions we specified at the top and solve for the constants (step 8). The answer is linear (step 9)! So there’s the answer: the temperature decay is linear.

But there are a couple things to consider here: first this is one-dimensional. We did that to make the math easy. With a real flame, the heat could go in any direction outward, basically in a spherical shape. Also we’ve specified that 20 cm away from the flame the temperature is 20 °C. This is often the case in the real world, because air is free to move around, and some distance from a flame there will always be cool air to be a heat sink. Problems like this can get really complicated if we want to calculate that distance from first principles, but it can be done!

The Clear Science staff is in the middle of administering a...

Mon, 20 May 2013 14:02:00 -0400

The Clear Science staff is in the middle of administering a Clear Science final exam. You’ve probably heard that internet company Yahoo bought Tumblr for $1.1 billion. Let’s talk some science about the number 1.1 billion.

In science, when you want to talk about big numbers, you use prefixes. Kilo means “times ten to the third power” or “times one thousand.” Every three more powers of ten gets another prefix, and they go like kilo, mega, giga, tera, etc. That means Yahoo bought Tumblr for 1.1 gigadollars.

People don’t usually talk about money with these scientific prefixes. But let’s ask ourselves, Clear Scientists: why not? We think it sounds cool.

(PS we’re still answering a heat transfer question, which we’ll come back to pretty soon.)

Finding the temperature decay from a heat source (like a flame)...

Tue, 07 May 2013 11:27:00 -0400

Finding the temperature decay from a heat source (like a flame) got us talking about heat flux. Heat flux is the movement of heat, and heat is going to flux away from the flame. Heat moves from high temperatures to low temperatures, and wherever heat goes it increases the temperature.

We called heat flux in the x-direction qx. Let’s draw a little box and call it a “system” and do what’s called a “heat flux balance” for the system.

In English: The heat flux into the box equals the heat flux out of the box.
In math: (qx at x) minus (qx at x+Δx) equals zero. Now divide both sides by Δx. Now take the limit as Δx goes to zero, which means the system width becomes infinitesimally small.
When you start saying “infinitesimal” you know you’re doing calculus. This is the definition of a derivative, and our balance ends up with “the negative derivative of heat flux in the x-direction equals zero.”

If you translate 3 back to English it says “heat flux is the same at every value of x.”

What we’re talking about right now is: What’s the...

Fri, 03 May 2013 14:00:30 -0400

What we’re talking about right now is: What’s the temperature decay rate from a hot point like a flame? To get there we stopped and talked about calculus a little bit though, because to do the answer justice we need some calculus. Stay tuned, we’ll be back on the case next week.

how are you? =)

Fri, 03 May 2013 12:55:05 -0400

The Clear Science staff is fair to middling, how about you?

So a derivative is like picking two points on a graph and...

Fri, 03 May 2013 10:49:40 -0400

So a derivative is like picking two points on a graph and calculating the difference in the y-values and dividing by the difference in the x-values … when the two points you pick are infinitesimally close. Up above we’ve drawn a plot of temperature T versus distance x, and we’ve shown the derivative at three points.

The way you can picture a derivative is this: If you draw a straight line that barely touches the curve at one point only, then that line is called a tangent. And the derivative at a point tells you the slope of the tangent. Where the curve is steep, the slope is high (3) and where it’s not steep slope is low (1/3). (The -ve signs are because temp goes down as x increases.)

We wondered what a derivative is. Imagine you have a graph with...

Wed, 01 May 2013 15:58:30 -0400

We wondered what a derivative is. Imagine you have a graph with temperature on the y-axis and x on the x-axis. If you pick two points on the graph you can calculate the difference in their y values and the difference in their x values. Dividing those, you would get ΔT/Δx.

In the top-left graph we pick two points far apart. Going from the first point to the second we move 3.1 spaces down on the y-axis, so that ΔT is -3.1. We move 5.5 spaces on the x-axis so that Δx is 5.5. Doing the math it’s -0.56.

But look, if we pick different points we get different values. In the top-right we get -1.67, and in the bottom-left we get -0.36. It depends on what two points we pick.

Now this is a derivative: what if we say the two points we pick are zero distance apart so essentially they are the same point? That is dT/dx, shown in the bottom-right. Each point on the graph will have a different dT/dx value, which is the derivative at that point.

This is now calculus btw, because we talked about two points zero distance apart. (Or an “infinitesimal distance apart” which means infinitely close together.)

Asking about the temperature near a hot flame we brought up an...

Mon, 29 Apr 2013 13:54:43 -0400

Asking about the temperature near a hot flame we brought up an important equation called Fourier’s law. The heat flux (q) away from a flame is a constant (k) times the negative of the temperature gradient. And we symbolized the temperature gradient with an upside down triangle in front of T.

That upside down triangle is called “del” and if we’re only worried about one dimension (the left-right dimension in the picture, which we’ll call the x-direction), this “del T” is the derivative of temperature with respect to that dimension. You write it dT/dx. You usually say it “dee-T dee-x” or “dee-T by dee-x.”

If you know calculus, you’ll recognize that is what we’re doing. It’s not really that complicated a concept though. So: What is a derivative, really?

Fourier’s law was first formulated by Jean Baptiste Joseph...

Fri, 26 Apr 2013 14:00:23 -0400

Fourier’s law was first formulated by Jean Baptiste Joseph Fourier, whose name is pronounced like “Foo-ree-ay.” The Fourier transform and the Fourier series are important concepts in math.

(Awesome animated math gifs if you click those, FYI.)

The Clear Science staff was going to answer the question...

Fri, 26 Apr 2013 06:44:37 -0400

The Clear Science staff was going to answer the question “Is there a decay rate in heat at distance from a flame/heat source?” To do that let’s consider one way that heat transports from one place to another: conduction.

Heat is energy. Say we have a flame on the left and no flame on the right. The flame is there because some chemical reaction is happening: chemical bonds are breaking and their energy is being liberated. Because of this the temperature of the flame is high, like 1500 degrees. On the right temperature is only room temperature or 20 degrees.

Heat moves by conduction from high temperatures to low ones. This is a basic property of the universe, and it is described by Fourier’s law. Written above in “math language,” what it says in English is “heat flux is proportional to the negative of the temperature gradient.” Or: heat fluxes from high temp to low.

Is there a decay rate in heat at distance from a flame/heat source? Ie 6 inches away from a fire that's burning at 1200 deg F is what temp? 12" inches? Etc

Wed, 10 Apr 2013 10:25:51 -0400

This is a great question, anonymous! And a complicated one, because heat is a weird thing that moves from one place to another in multiple ways. When heat is absorbed by a substance, it raises the temperature of that substance. Heat can move by conduction, convection, and radiation.

In the coming days, the Clear Science staff will try to unpack this a little and throw some clarity on it.

But with the chlorine trifluoride, wouldn't you run the chance of high temperatures and the expelled oxygen creating fire in a carbon-rich environment?

Thu, 04 Apr 2013 10:42:00 -0400

The Clear Science Staff made no predictions about how pretty it would be! We will go out on a limb and say you’ll get some fluorides in the products.

Someone try this at home with ClF₃ and tell us what happens. (DISCLAIMER: Don’t ever try this at home, never touch ClF₃ unless you’re being paid well for it.)

Perhaps you could burn glass with chlorine trifluoride?

Thu, 04 Apr 2013 09:13:22 -0400

Chlorine trifluoride (ClF₃) is a truly horrible chemical, which will in fact react with glass. What it does isn’t so much “burning” which is an oxidation, but is rather fluorination. This means it will strip the oxygens off the silicon atoms and add fluorine instead, making silicon fluoride compounds.

A common use of chlorine trifluoride is to fluorinate uranium, which is the first step in reprocessing nuclear material. This turns the uranium into uranium hexafluoride (UF₆).

Maybe the anon means this: www(.)starfiredirect(.)com/fire-glass. Or another site: www(.)blazingglass(.)com/fire-crystals/ Perhaps I'm too stupid and overread it, but I couldn't find out yet how it works. This can't be /real/ glass or can it?

Wed, 03 Apr 2013 10:45:53 -0400

Hey anonymous, good question. We were talking about whether or not you could burn glass, and the Clear Science Staff said glass is an oxide already so it’s kind of pre-burned in a sense. This link is to a company that sells “fire glass.” What that is is small glass particles that sit in a fireplace, as a replacement for those fake logs you sometimes see.

The glass itself doesn’t burn. Rather, its a porous solid medium for natural gas to percolate through. The natural gas (mostly CH4) comes up through the glass particles, and it’s the CH4 and other gases that burn. The glass is just something to look pretty.

There’s some science to this, because if you heat up regular glass like that it could pop and break due to thermal expansion. Because of that, glass needs to be tempered the right way to allow it to experience big changes in temperature.

wockerjabby: broccoli! Hey Clear Scientists, can you picture...

Mon, 01 Apr 2013 10:00:15 -0400

wockerjabby:

broccoli!

Hey Clear Scientists, can you picture what this awesome gif is showing? Let’s say you define a piece of broccoli in cylindrical coordinates, so it runs lengthwise in the axial (z) direction. This gif is a cross-sectional scan of the broccoli in the axial (z) direction, with each frame showing you planes of constant z. In each plane the position of the broccoli is a function of the other two dimensions, which in cylindrical coordinates would be r and θ.