Thermal Expansion of aluminium

[newtonlovechild]

Hi,

The coefficient of thermal expansion for aluminium is 23ppm/C at 20C = 0.000023m per degree in temperature (C).

Is this temperature:

(1) the temperature of the air circulating around the material in the sun,
(2) the temperature in the shade at that time of the day, or
(3) the tactile temperature of the material?

This might seem like a simple problem for Newton's love child, but I suspect I'm illegitimate. :)

N

 

[Bystander]

Think it over --- is it going to be the temperature in the lobby of the local movie theater?

 

[newtonlovechild]

Think it over --- is it going to be the temperature in the lobby of the local movie theater?

it's going to be the temperature of either the material or the air, but I'm not sure which.

[Mentor's note: edited to keep the thread on-topic]

 

[Nugatory]

it's going to be the temperature of either the material or the air

Right.

but I'm not sure which.

What do you think and why? You might try considering the situation in which the aluminum starts colder than the air (we just took our piece of metal out of the refrigerator) and gradually warms up to air temperature. What do think the the expansion/contraction behavior will be?

 

[newtonlovechild]

Nugatory

It will expand until it reaches the air temperature. But the air temperature in your kitchen will be cooler than outside in the sun or the shade - where the temperature for a given place is measured. What I'm getting at is, if an engineer wishes to calculate the expansion of a material for a proposed building in a city where the temperature in the shade ranges between 5C and 35C, does he base the calculations on the shade temperature, the temperature out in the sun, or the tactile temperature of the material, seeing that dark objects reflect less light and therefore become hotter? For example, a steel beam out in the sun will become hotter and thus expand more than when in the shade, and a black steel beam will become hotter and thus expand more than a white steel beam, even if the air around them is the same temperature.

N

 

[Chestermiller]

Does it make sense to say that, if the air is hotter than the material, the material will expand even before it has heated up?

Chet

 

[newtonlovechild]

Chet,

No, the material should expand in proportion to the effect the air temperature has on it. So if the air temperature is 20C, aluminium will expand at 0.000023m per linear metre per degree of temperature change. But there is a difference between shade and solar temperature, solar temperature being up to 8C hotter than shade temperature. So, are thermal expansion coefficients based on solar or shade temperatures? Also, a black material will become hotter than a white material, not because of the ambient air temperature but because of its lower reflectivity. If the thermal expansion coefficient formula for aluminium were applied to two equal lengths, one black the other white, the expansion will be the same according to the formula, but the black length will in fact have expanded more under the same temperature due to it being hotter. This is why I asked about the tactile temperature of a material.

N

 

[Chestermiller]

The material expands in response to the temperature of the material. It has nothing to do with the surrounding environment or how the environment causes the temperature of the material to change.

Chet

 

[newtonlovechild]

Chet,

If the temperature in the city where I live was 30C maximum at 3pm today and I want to calculate how much a 10m length of aluminium in my back yard, under direct sunlight, had expanded at that time, the answer would be (30-20) * 0.000023 * 10 = 0.0023m. But this is 30C at the weather station, not my back yard. Now, even if I had my own weather station in my back yard and I measured 30C at 3pm, this would still be the air temperature at my weather station, and not the solar temperature surrounding the aluminium, which will be a few degrees hotter. I guess what I'm asking is, if a length of aluminium is standardized at 20C, do I assume that the temperature value should also be standardized, i.e. the temperature in the shade should be used?

N

 

[Vanadium 50]

Why are you arguing with the correct answer? Chet is right - it's the temperature of the material that matters. Bringing in the temperature at some weather station somewhere else needlessly complicates things.

 

[newtonlovechild]

Vanadium 50,

I'm not arguing. I agree with Chet; yes, the material expands or contracts in proportion to its temperature. But its temperature is governed by the temperature of the air surrounding it, so as the air heats up so does the material, and it expands. But to predict the linear expansion of the material requires inputting a temperature into the formula. If an engineer wants to predict how much linear expansion there will be in a proposed steel bridge at a given location, he needs to know how hot the steel will get. I assume he needs to know the air temperature for that location so he can calculate how hot the steel will get and thus calculate the width of expansion joints. Am I right? If so, I assume the engineer will base his calculation on the worst scenario. But what if he wants to know the linear expansion of steel in the open air at precisely 30C? Does he input into his formula the 30C shade temperature, or the approximated solar temperature surrounding the steel (say 35C), or does he measure the tactile temperature of the steel (say 40C)?

N

 

[Vanadium 50]

You most certainly are arguing. You want the temperature of the material. Not the air surrounding the material, not the temperature where it's sunny and the bar is in the shade, or shady when the bar is in the sun, or down the road at the weather station, or any other thing. You want the temperature of the material, and not anything else. If you don't know the temperature of the material, I agree that's a problem, but that's a problem that is unrelated to how thermal expansion works. You'd have the same problem with "how much does a spring stretch if I put an unknown weight on it?"

 

[Chestermiller]

Vanadium 50,

I'm not arguing. I agree with Chet; yes, the material expands or contracts in proportion to its temperature. But its temperature is governed by the temperature of the air surrounding it, so as the air heats up so does the material, and it expands. But to predict the linear expansion of the material requires inputting a temperature into the formula. If an engineer wants to predict how much linear expansion there will be in a proposed steel bridge at a given location, he needs to know how hot the steel will get. I assume he needs to know the air temperature for that location so he can calculate how hot the steel will get and thus calculate the width of expansion joints. Am I right? If so, I assume the engineer will base his calculation on the worst scenario. But what if he wants to know the linear expansion of steel in the open air at precisely 30C? Does he input into his formula the 30C shade temperature, or the approximated solar temperature surrounding the steel (say 35C), or does he measure the tactile temperature of the steel (say 40C)?

N

You are asking how an engineer performs heat transfer calculations, including (possibly) convection, radiation, and conduction. That's a separate subject that, apparently, you haven't studied yet. Suffice it to say that the engineer can employ his knowledge of heat transfer to estimate the temperature of the material in any of the situations you are describing, including the transient and spatial variations of the temperature within the material.

Chet

 

[Astronuc]

he needs to know how hot the steel will get.

Exactly! The thermal expansion of a material is dependent on the temperature of the material. The environmental temperature will have an influence on the temperature of the material (aluminum metal in this case), which will try to reach thermal equilibrium with the environment by virtue of various heat transfer phenomena - e.g., conduction, convection (with the air) and radiation - as Chet indicated. Sunlight would heat a metal above the ambient air temperature. The air near the surface of the material being heated will be warmer than the air several feet away.

 

[newtonlovechild]

Van 50,

You are entitled to your opinion regarding me arguing, but you can't be certain. I thank you for your contributions but I feel it's best that you don't contribute any further.

If anyone else is able to understand what I'm asking I'd appreciate your contributions. To me my question is straight forward but perhaps I'm not explaining it right. I honestly don't know how else I can put it. Perhaps my question should be: How do engineers predict how hot the steel in a proposed bridge will get in a given geographical location in order to predict thermal expansion?

N

 

[Chestermiller]

Van 50,

You are entitled to your opinion regarding me arguing, but you can't be certain. I thank you for your contributions but I feel it's best that you don't contribute any further.

If anyone else is able to understand what I'm asking I'd appreciate your contributions. To me my question is straight forward but perhaps I'm not explaining it right. I honestly don't know how else I can put it. Perhaps my question should be: How do engineers predict how hot the steel in a proposed bridge will get in a given geographical location in order to predict thermal expansion?

N

Isn't that what I addressed in post #13? You can't be taught an entire course in heat transfer within the framework of Physics Forums. So, if you want to know the answer to your question, take a course in Heat Transfer.

Chet

 

[newtonlovechild]

This is becoming hilarious!

Chet, I think my last post was being typed while you and Astronuc were sending your posts, hence my odd reply. :)

I thank you and everybody else for your contributions. I'm obviously not an engineer or a physicist, but as a surveyor I work with an aluminium levelling staff from time to time. In all my training nothing was mentioned about thermal expansion of the staff and its effects on station heights, which, as I’ve recently researched, can be in the range of centimetres, and this can be significant for some projects.

The formula for aluminium staff expansion is:

[Tf - Ts] * measured height * 0.000023m/C where Tf = temperature in the field and Ts = temperature of the standardized staff (15C).

I then wondered about the field temperature; is it the shade temperature or the solar temperature, as they are different. I therefore researched further but couldn’t find anything. Hence I came to this forum for assistance. I understand that thermal expansion has to do with the temperature change of the material, but the material is affected by the ambient air temperature. For example, the air temperature might be 40C in the shade and 45C in the sunshine, but the staff temperature (which is in the sun) might be 50C. So, how to apply the Tf isn’t clear to me.

But perhaps I need to ask: Is there a table that shows how hot different metals get under different ambient conditions? If I can confirm the temperature aluminium will get to in the sun when the shade temperature is 40C, I can perhaps accurately compensate for thermal expansion.

I hope this makes it clearer, and I apologise if I have failed to do this previously.

N

 

[Bystander]

Finally, a context. What's the listed accuracy of the level on your telescope/theodolite, whatever you're using for levelling shots?

 

[RobS232]

Van 50,

You are entitled to your opinion regarding me arguing, but you can't be certain. I thank you for your contributions but I feel it's best that you don't contribute any further.

If anyone else is able to understand what I'm asking I'd appreciate your contributions. To me my question is straight forward but perhaps I'm not explaining it right. I honestly don't know how else I can put it. Perhaps my question should be: How do engineers predict how hot the steel in a proposed bridge will get in a given geographical location in order to predict thermal expansion?

N

As somebody who has actually carried out such calculations, using finite element programs (FEA), let me try to explain it to you. The expanding material only expands according to the temperature it is at. But, as you point out, this is not known in a dynamic situation. The surrounding temperature is rising and transferring heat to the material and the metal material gets hotter more quickly in some areas than others via heat transfer. There may be a shaded area that heats more slowly, or even dumps heat from the metal into a cooler shaded air. Later on, the day starts cooling and the process reverses. A complete model takes all of these factors into account and calculates the change in shape of the material as it expands unevenly. The models are quite accurate in their predictions and widely used for complex problems, such as jet engines. Since the problem you describe likely never achieves equilibrium (all of the metal never achieves air temperature before cooling starts) assuming that it does likely overestimates the expansion. I CAN be certain that a simplified assumption will not be accurate. .

 

[Sivasakthi]

Hi..
What I wish to say is that the temperature that you measure is an average quantity right? It is that due to the self vibrational energies of all the atomic constituents in the material. When you expose it to more heat, it increases their vibrational energies and these vibrations on an average determines the temperature. I should say that a lot more contributes to the heat transfer; like the imperfections or the dislocations that the material has internally. You can't get rid of these defects, and they are the carriers of heat through the material.
And then how strong a material can be heated without breaking or fracture do depend on the atomic interactions and non localization. It is that when you give more heat, the bonds break ( we say dislocations climb up ). So what happens to the atoms? Their bond breaks and so the enthalpy and hence the free energy of the material increases ( atoms when bonded has less energy than they are separated ). This makes them to occupy the vacancies , thereby reducing the volume. On the other hand if the atoms bond each other, more vacancies are created in the atomic realm and this increases the volume. That is, the size of the material changes. Hence, these are all the properties of the material. To know more about, I guess, it needs more terms from statistical mechanics and condensed matter.
I don't know if this can help you.
SS

 

[Chestermiller]

Hi..
What I wish to say is that the temperature that you measure is an average quantity right? It is that due to the self vibrational energies of all the atomic constituents in the material. When you expose it to more heat, it increases their vibrational energies and these vibrations on an average determines the temperature. I should say that a lot more contributes to the heat transfer; like the imperfections or the dislocations that the material has internally. You can't get rid of these defects, and they are the carriers of heat through the material.
And then how strong a material can be heated without breaking or fracture do depend on the atomic interactions and non localization. It is that when you give more heat, the bonds break ( we say dislocations climb up ). So what happens to the atoms? Their bond breaks and so the enthalpy and hence the free energy of the material increases ( atoms when bonded has less energy than they are separated ). This makes them to occupy the vacancies , thereby reducing the volume. On the other hand if the atoms bond each other, more vacancies are created in the atomic realm and this increases the volume. That is, the size of the material changes. Hence, these are all the properties of the material. To know more about, I guess, it needs more terms from statistical mechanics and condensed matter.
I don't know if this can help you.
SS

RobS232, What do you think of this?

Chet

 

[RobS232]

Hi..
What I wish to say is that the temperature that you measure is an average quantity right? It is that due to the self vibrational energies of all the atomic constituents in the material. When you expose it to more heat, it increases their vibrational energies and these vibrations on an average determines the temperature. I should say that a lot more contributes to the heat transfer; like the imperfections or the dislocations that the material has internally. You can't get rid of these defects, and they are the carriers of heat through the material.
And then how strong a material can be heated without breaking or fracture do depend on the atomic interactions and non localization. It is that when you give more heat, the bonds break ( we say dislocations climb up ). So what happens to the atoms? Their bond breaks and so the enthalpy and hence the free energy of the material increases ( atoms when bonded has less energy than they are separated ). This makes them to occupy the vacancies , thereby reducing the volume. On the other hand if the atoms bond each other, more vacancies are created in the atomic realm and this increases the volume. That is, the size of the material changes. Hence, these are all the properties of the material. To know more about, I guess, it needs more terms from statistical mechanics and condensed matter.
I don't know if this can help you.
SS

Thermal expansion is a macroscopic property and does not need a microscopic interpretation in order to make a calculation. Heating a material will not cause it to break, unless it is constrained, and mechanical stresses are imposed. Even then, analyses using fracture mechanics depend on empirical rules, rather than first principle analysis.

 

[Chestermiller]

Thermal expansion is a macroscopic property and does not need a microscopic interpretation in order to make a calculation. Heating a material will not cause it to break, unless it is constrained, and mechanical stresses are imposed. Even then, analyses using fracture mechanics depend on empirical rules, rather than first principle analysis.

Yes. Nicely said. This was my perspective also.

Chet

 

[Sivasakthi]

Actually what I focussed was in the size variation.Yeah mechanical stresses are needed for fracture. What I wished to point out was the role of defects or dislocations. They act as carriers of heat as well as for the fracture of materials upon the action of mechanical force.

 

[Chestermiller]

Actually what I focussed was in the size variation.Yeah mechanical stresses are needed for fracture. What I wished to point out was the role of defects or dislocations. They act as carriers of heat as well as for the fracture of materials upon the action of mechanical force.

I hate to say this man, but all this molecular explanation is going to do is confuse the OP. He was looking for a continuum answer, and, in my judgement, your molecular description muddied the waters. Yes, the molecular effects are ultimately responsible for the macroscopic continuum properties that are measured experimentally, but so what. If the continuum macroscopic properties are known from experiments, then the mechanistic molecular cause of these properties becomes moot. Please use better judgement in future posting.

Chet

 

[Windadct]

It seems there are really 2 issues here discussed ( or asked as one). 1) The Thermal Expansion of a material is solely dependent on its own temperature. 2) What temperature a material is, or will be under various conditions is dependent on many factors, and these are independent of Thermal Expansion.

Considering - Actual Aluminum Alloy used
Finish ( clean aluminum or black anodized)
Ambient Air temp
Air flow
Altitude and Humidity
Strength of Sun (eg. latitude)
Incident angle of the sun to the staff

There are engineers who's full time job is dealing with this... IMO assume ambient air temp - the sun does not shine on both sides of the staff and aluminum has good thermal conductivity - so one side may be heated by the sun the other side will radiate and conduct heat to the air.

For a 2 M aluminum staff - it will not be centimeters.

However if you are asked to place anchors in one material (say cement CTE 10m/mK 10^-6)) to which a long beam will be set (say aluminum 22) -- and the temperature in the location may change dramatically - the effect of the CTE should be in the back of your mind. Esp when the customer calls screaming that the beam does not fit!

Also why bridges are not hard bolted ( typically left floating on a locating pin / bolt, or rollers) to their mounts and they have expansion joints. That is all part of the job of the bridge engineer. The methods of construction ( suspension and trestle for example) also help minimize the effect of the CTE. You see the same thing in long pipe runs - the mounts are on rollers and every no and then a jog or "u" is added to allow some flex - to absorb the changes in length.