Talk:Coefficient of thermal expansion

Please have someone qualified write this article

This article is full of incorrect physics. For example the concept of the linear coefficient of expansion belongs in the realm of classical physics. There is no simple explanation on an atomic level. One needs to know about crystal structures, amorphous materials, quasi-crystals, etc. My suggestion is to get rid of the explanation and just refer to the observed effect in classical physics. Another example is the reference to freezing water -> ice. The is a phase change effect and is explained by molecular arrangement as water beings to form a crystal structure. It is specific to a subset of materials and alloys, thus there is no general rule for a phase change.

Also there is no need to bring partial derivatives into this discussion. The average reader will not understand it. Please reformulate the expressions without the use of calculus. For example

  L(T) - L(To) = L(To)*( a )*( T - To)    

and this only applies over a finite temperatue range, since there are non-linear second order effects. Wiseoldowl 16:01, 28 October 2007 (UTC)

Answer: The person that wrote this article IS qualified. The writer was careful to include the caveat in his equations that he was referring the CTE at 20C. The fact that CTE is not linear in many materials does not negate the theoretical accuracy of the equations. It might have been helpful if the writer had gotten into the discussion of non-linearity of materials but that may have muddied the waters. Anyone that would be interested in using these equations would of necessity have to understand the use temperature range and the non-linear properties of a given material before calculating the CTE. —Preceding unsigned comment added by 24.152.155.130 (talk) 05:31, 15 November 2007 (UTC)

Sorry to differ with you on this discussion. I learned about the thermal coefficient of expansion TCE as a freshamn in high school at the age of 13 when I took a foundary course. It is commonly used in foundaries where the shrinkage due to a cooling cast of metal must be accounted for. Please see the Wiki article on "Casting". Do you think that all workers in foundaries are well versed in partial differential mathematics. Now as a scientist and mathematician, it is my experience that partial differential equations are not normally taught until at least the later years of high school, or the first or second years of college. However, TCE is one of the first things that is taught in introductary courses in classical physics. Last, within the field of classical physics there is no theoretical derivation for the TCE, it is only an observed, experimental effect. Any attempts to derive a TCE need to be based on the atomic structure and chemical compositon of the material in question. A simple example is a bimetallic strip. For references you may wish to look up Arnold Sommerfeld's "Lectures in Theoretical Physics - Vol. 5" pp 3.

Regretfully I must agree with the first commenter. Not only is the use of partial derivatives unnecessary, the author demonstrates a lack of understanding of what a derivative (of any kind)is -

"alpha = (1/Lo) dL/dT where is the original length, the new length, and the temperature."

In dL/dT or its partial equivalent L and T do not have the significance attributed to them. L and T are general concepts of length and temperature, not particular values of length and temperature. Andrew Smith —Preceding unsigned comment added by 82.32.50.77 (talk) 15:43, 26 November 2009 (UTC)

I have tried to rewrite the article taking into account the above comments. I have tried to limit the amount of calculus, or at least keep it separate from the main explanatory sections. Ultimately, the coefficient of thermal expansion cannot be understood without a rudimentary understanding of the derivative. Much of the previous article was thrashing around due to an incomplete or improper understanding of this concept. Hopefully those who are not familiar with the limiting process and derivatives will be able to make some sense of the article and those who are can find it useful as well. Its not perfect, but its a start. PAR (talk) 19:32, 26 November 2009 (UTC)

Please improve

how was this formula found, the experiment used, the person

not satisfactory explanation of equations, could use an actual example

paranoir@yahoo.com

• Query: What does "The expansion of a crystalline material occurs only when the force field of the crystal deviates from a perfect quadratic. If the force field is perfectly parabolic, no expansion will occur." mean? In particular, what is the "force field" of a crystal?? How is this relevant to this article? Perhaps this sentence needs to be deleted.

The template

We need to find out the names of the different versions of the coefficient. The final authority is IUPAC according to Wikipedia. PAR 22:56, 20 December 2005 (UTC)

Length

What are the units for length? inches or millimeters?

it is unitless. if you notice in the formula there is length on the top and bottom, so they cancel out, leaving you with 1/K for the units. thus the units for length you use doesnt matter only the ratio of the expansion to the original length.

It would be nice

IT WOULD BE NICE TO HAVE A DIFF IN TEMP AND MULTIPLY THIS BY VOLUME TO GT THE VOLUMETRIC EXPANSION OF THE FLUID

Also, some temperature dependence would be nice, i.e. how does the CTE typically change as a function of temperature? How constant is it over a wide range of T? Walter Spieksma 15:48, 19 February 2007 (UTC) Except for water below 4°C, CTE of liquids rises with temperature. CTE depends on density (r) according to CTE=⌂r/(r⌂T).

Improving the phenomenological explanation

The first two senctences try to describe why there is a dimensional change with temperature change. They say

"During heat transfer, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bond"

I find this as a hand waving explanation. I think that the explanation I offer below is a far superior, but I find myself bad at incorporating it into the article. Here is the explanation:

If a material is heated or cool, then energy has been imparted to the material proportional to its heat capacity. So, if you heat a particle it becomes more energetic. Now energy is related to velocity through E=1/2 m v². This means that particles are now moving faster. In particular the atoms are moving faster.

First, examine a solid; all atoms in solid form vibrate, and they do so at approximately 10¹³ Hz. When more energy is imparted to them they change their velocity, but not their frequency. This means the amplitude of their vibrations is larger. Hence their atomic spacing is larger.

Now if we apply the logic to the fluid phases (i.e. gases and liquids), we find that the atoms or molecules are actually traveling faster. So for molecules in air, the time of their mean free path is now shorter, or in other words, they have more collisions for a give time. Collisions can be with other gas molecules or with another phase (such as the walls of a container). Now the number, frequency, and energy of those collisions determines the pressure. As we no, the pressure is related to the volume through the the natural gas law. The same hold true for liquids, but instead of think of linear motion, rotational motions become more prominent.

Can someone add that explaination in a more eloquent form? Walter Spieksma 15:48, 19 February 2007 (UTC) This line of argument would have to be found for density as well. However, this is not the case. The Rackett equation to calculate density as a function of temperature or the Benson group estimation method to calculate density from molecular formula are known methods involving empirically fitted parameters only. In reality, bond length is not the only factor, the way molecules can be packed together in a liquid or solid also plays a role which is hard to adress theoretically. Between molecules in a liquid a vacuum exists up to several volume percent.

Confusion

There are two beta, one for the Compressibility, and one for the volumetric thermal expansion coefficient. This can lead to confusion. —The preceding unsigned comment was added by 195.68.31.231 (talk) 08:54, 7 March 2007 (UTC).

Removing "hello!!!!!" from first line

I can't seem to figure out how to remove the "hello!!!!" someone put up on the first line, i don't want to revert back to an older version of the article because i am not sure what has been accepted as a current change and what has not. If anyone can remove that hello it would be great.

coeffecient of thermal expansion of steel

I have come across different sources that give different values for the coeffecient of thermal expansion of steel(just steel only). Some state it as 12.0, some 13.0, while this article states it at 11.1. So am I right to say that it is variable due to the different compositions of steel(since it is a mixture)? Please correct me if i'm wrong. Thanks AquaDTRS (talk) 15:11, 1 February 2008 (UTC)

There are many kinds of steel. 155.212.242.34 (talk) 14:39, 15 April 2008 (UTC)

α₁, α₂

I've seen materials listed with two alpha values, α₁, and α₂ for ASTM-E831 CTE values. What do these mean? 155.212.242.34 (talk) 14:41, 15 April 2008 (UTC)

Probably found the information already, but here are my 2 cents: Alpha1 - thermal expansion rate at the temperatures below Tg (Glass transition temperature) Alpha2 - thermal expansion rate at the temperatures above Tg (Glass transition temperature) reference to LOCTITE data-sheet with a bit more details: www.g4e.cn/wordpress/wp-content/uploads/2008/12/3517-en.pdf‎

FYI i've seen it where: ALPHA1 = Flow direction ALPHA2 = Transverse direction

Autodesk uses this metric: https://knowledge.autodesk.com/support/inventor-products/learn-explore/caas/CloudHelp/cloudhelp/2014/ENU/Inventor/files/GUID-A79E3FE2-EE6E-4569-9CA3-6995CCF2E4CE-htm.html — Preceding unsigned comment added by 199.189.240.95 (talk) 19:32, 18 April 2019 (UTC)

Different equation...?

I've just done a large amount of research on thermal expansion coefficients and I've been told to use the following equation (fingers crossed--don't know if this'll work!): $p_{1}={p_{0} \over (1+(\beta (\Delta _{t})))}$ , where:

• β = coefficient of thermal expansion
• p₁ = final density
• p₀ = initial density
• Δ_t = change in temperature (final temperature - initial temperature)

Should we include this one??

We can add it as long as you have a reference for it. Wizard191 (talk) 12:32, 23 April 2010 (UTC)

How's this?

Yeah, that's a good ref. Please add the equation. Wizard191 (talk) 21:55, 26 April 2010 (UTC)

Volumetric expansion coefficient

The article states "For exactly isotropic materials, the area thermal expansion coefficient is 2/3 of the volumetric coefficient.". Now, i'm pretty sure that's wrong, i believe the right figure is that the area thermal expension coefficient is one third the volumetric coefficient. Larryisgood (talk) 17:12, 2 May 2010 (UTC)

In fact it definitely is 1/3. Larryisgood (talk) 17:40, 2 May 2010 (UTC)

I am entirely wrong, i thought the article was claiming the volumetric coefficient was 2 thirds the linear coefficient.Larryisgood (talk) 21:43, 3 May 2010 (UTC)