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May 03, 2013
215 notes
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.)

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.)

Tags: science math calculus tangent derivative

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May 01, 2013
351 notes
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.)

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.)

Tags: science math calculus derivatives physics

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April 29, 2013
58 notes
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?

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?

Tags: science math derivatives physics heat transport heat flux Fourier's law heat

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April 26, 2013
14 notes
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.) 

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.) 

Tags: science Fourier heat transport physics math

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April 26, 2013
227 notes
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.

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.

Tags: science heat energy conduction Fourier's law physics flames fire math

Text
April 10, 2013
9 notes

Anonymous asked: 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

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.

Text
April 04, 2013
9 notes

Anonymous asked: 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?

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.)

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April 04, 2013
17 notes

Anonymous asked: Perhaps you could burn glass with chlorine trifluoride?

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).

Text
April 03, 2013
5 notes

Anonymous asked: 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?

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.

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April 01, 2013
118 notes
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.  

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.  

(via bluishorange)

Tags: science math broccoli food imaging