This vCalc dataset, Temperature Coefficients of Expansion, is used in several vCalc equations via a look-up equation, Temperature Coefficient of Expansion Lookup.  The data provided here represents the Temperature Coefficients of Expansion for over 185 different materials.

Data Fields

Two columns are provided and are named as follows:

• Product_or_Material - the name of the material for which you're performing a look-up of the expansion coefficient
• Temperature_Expansion_Coefficient - the coefficient of expansion provided in units of `10^-6 m/(m*K)`

Description

Heating or cooling a material causes its length to change.  This linear change is proportional to both the original length and the temperature change. This coefficient expressing the linear proportionality for thermal expansion can be looked-up using the equation: Temperature Coefficient of Expansion Lookup.

The units of the Temperature Coefficient of Linear Expansion are 1E-6 m/(`m*`^oK), which, of course, simplifies to units of 1E-6/^oK.

Usage

There are many applications for computing the expansion of a material in construction, in manufacturing, in physics experiments, in materials research, etc.  Here are some example applications:

Concrete

When constructing a concrete floor surface -- let's say for a large storage building -- the temperature changes experienced by the concrete could be significant, depending on where the concrete is located.  Equally significant expansion and contraction can occur in the concrete pads.  To make certain that you have a properly-sized expansion joint between pads you can calculate the change in linear dimension of the concrete slab over a typical temperature range for your geographic region. From this data set we can get the coefficient for concrete, which is `14.5E-6 m / (m*K)`.

For Tulsa Oklahoma, as an example, the average high in July and August is 93.1 ^oF¹.  The lowest of the monthly averages is January with 27.5 ^oF² .  So, using this range for the temperature inputs to the Expansion Due to Temperature equation and assuming a 10 ft X 10 ft slab (the slab length or width being the expansion direction we want to check), the Expansion Due to Temperature equation would tell us that we would need to provide an expansion joint between the pads that would support a change in width or length of at least: 0.06 inches, which is a little more than a 20th of an inch.

Actually you could be even more precise and perform the calculation using the temperature on the date the concrete was poured and the average high temperature, since initial length will be that length at the temperature you initially cured the concrete.

Plumbing

Just like the concrete example above, you might want to check the possible expansion of a run of copper pipe to determine a reasonable offset from the wall frame member where the pipe turns.  The length L would be the entire length of the pipe, including the bend in the pipe at both ends.  The temperatures inputs to the Expansion Due to Temperature equation would be the extremes to which the pipe might be exposed and, of course, the selected material would be Copper.

From this Data Set we can find that the coefficient of expansion for Copper is: `16.6E-6 m / (m*K)`.

If we used the same average high and average low temperatures from the Tulsa Oklahoma temperature above, the Expansion Due to Temperature equation tells us that a forty foot run of copper pipe could expand as much as 0.363 inches in Tulsa's temperature range. So, you would be safer to provide offsets of at least this much to accommodate possible expansion. You could of course, offset the pipe on both ends, first rounding the 0.363 inches up to a half inch and then your safe offset on either end would be approximately a quarter inch.

Manufacturing

Fabrication processes may often require fairly stringent adherence to size specifications and thus estimating the expansion due to temperatures a component can experience during fabrication could play an important role in quality control.

An interesting example of the expansion requirements on an aircraft  can be observed in the extreme case of the SR-71.  The surface of this aircraft would exceed 500 ^oF at full velocity and the largest part of the aircraft was constructed of Titanium.  From this Data Set we can find that the coefficient of expansion for Titanium is: `8.6E-6 m / (m*K)`. The aircraft actually leaked huge amounts of fuel on take-off because of the fabrication design of the fuselage, with fuel spilling out until, once in flight, the surfaces could heat up enough to expand and seal the leaking of the fuel cell.³  The Titanium used for the SR-71's fuselage was an allow but if the fuselage had been constructed of pure Titanium, our equation tells us that a 25 foot panel of fuselage would subjected to a 430 ^oF temperature change would expand approximately 0.09245 inches (almost a tenth of an inch)

See also

• Expansion Due to Temperature
• Expansion Due to Temperature (with Material Lookup)

1. ^ http://www.srh.noaa.gov/tsa/?n=climo_tulsacli
2. ^ http://www.srh.noaa.gov/tsa/?n=climo_tulsacli
3. ^ http://iliketowastemytime.com/facts-you-didnt-know-about-sr71-blackbird