# How to Calculate the Coefficient of Linear Expansion

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Many materials and substances, such as steel, expand given an increase in temperature. The coefficient of linear expansion measures the change in length that corresponds to a change in temperature. Generally, lab technicians and researchers perform tests to determine the extent of this expansion. They start with the material at a given length and temperature, and then increase the temperature and watch how the material expands. They end up with the original length at the original temperature and the ending length at the ending temperature. From this data, it's possible to determine the coefficient of linear expansion.

### Things You'll Need

• Calculator
• Locate or produce test data. You need data that illustrates how the original length of the material you are interested in expands with a change in temperate. This data is needed to calculate the coefficient of expansion. You can find this data from previous coefficient of linear expansion measurements made on the material in question from laboratory or manufacturing test results. If you can't find the data, perform the test yourself. The test basically involves placing the material in a chamber where you can increase the temperature until the material expands. You record both the original length and temperature and the ending length and temperature. The specific procedures and test setup depend on the material type and size.

• Find and record the original length of the material (L1) at the original temperature (t1). Refer to the test data from step 1.

• Find and record the ending length of the material (L2) and the ending temperature (t2). Refer to the test data from step 1.

• Calculate the coefficient of expansion (COLE) using the formula COLE = (L2-L1)/[L1 (t2-t1)]. For example, if L1 is 10 inches at t = 75 degrees F and L2 is 15 inches at t2 = 110 degrees F, then COLE = (15-10)/[10(110-75)] = 5/[10(35)] = 5/350 = 0.0143

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