Expansion-Contraction Coefficients

Almost without exception, solids expand upon heating and contract on cooling. 

The table given below shows the change in length (expansion or contraction) when a 

unit length (1 m or 1 ft, etc) of a material is warmed or cooled one Celsius degree. 

This fractional change in length for a temperature rise of 1° is called the COEFFICIENT 

OF LINEAR EXPANSION. For example, 1.00 m of steel increases 2.00 E - 5 m when it is 

warmed 1° C. Consider a bridge 1.00 E 3 m long. For every increase in temperature 

of 1° C every meter of the bridge increases by 2.00 E‑5 m. This results in a total 

of 2.00 E - 2 m increase in length. When the temperature increases by 10.0 degrees 

the increase in length will be 10 times as much. And between winter and summer, 

a change of temperature of as much as 40.0° may take place, increasing the length 

of this bridge by 0.800 m (1.00 E 3 m x 40.0° C x 2.00 E - 5 /° C ). If the engineer did not 

allow for expansion, the force exerted by this expansion (or contraction in winter) 

would result in buckling of steel girders.

 

In metal rods or wires, the expansion or contraction that engineers are concerned 

about is essentially in one dimension -- length (if you were dealing with a block of 

metal, you could observe expansion or contraction in three dimensions). In a liquid, 

however, the expansion or contraction in three dimensions in always important. 

Therefore the figures in the table for the expansion of liquids express the COEFFICIENT 

OF CUBICAL EXPANSION the change in volume for a unit volume (liter, gallon, etc.) 

of a liquid changing one Celsius degree in temperature.

 

You cannot easily observe the effects of temperature change on gases unless the 

gas is sealed in a container. The gases of the atmosphere are free to move when 

expanding or contracting. However, experimentation has shown that unlike solids 

and liquids, all gases expand and contract to the same extent with a change in 

temperature. That is, all gases have the same coefficient of expansion or contraction.

 

The behavior of substances as the temperature changes gives us another 
means of identifying them. Solids melt and liquids boil; if they are pure substances, 
they melt or boil at definite temperatures. But whether or not these changes occur, 
matter in all states expands or contracts with a change in temperature, and the extent 
of this change can be measured. Melting points, boiling points, and the amount of 
expansion or contraction are three properties useful in distinguishing among substances,
but some substances neither melt nor boil. Still other properties are needed to distinguish 
between them.

 

Problems:

1. Using the tables (below), determine what change in length or volume results when:

a. an aluminum rod 1.00 m long is warmed 1.00° C:

b. a glass rod 5.00 m long is warmed 2.00° C:

c. 10.0 m of platinum wire are cooled 5.00° C:

d. 2.00 L of grain alcohol are cooled 10° C:

e. 1.00 L of benzene is warmed 5.00° C:

2. Using the tables, to what temperature must a steel rod 1.00 m long at 20.0° C 
be heated to increase in length by 1.00 E - 4 m?

3. An unmarked volume of a liquid was warmed from 20.° C to 30.° C. This resulted 
in an increase of 0.107 L. The coefficient of cubical expansion of the liquid
 was 5.1 E - 4/° C. What was the original volume of the liquid?

 

Table of Coefficients of            Table of Coefficients of
Linear Expansion - SOLIDS         Cubical Expansion - LIQUIDS

aluminum     2.3 E - 5/° C            grain alcohol    1.12 E - 3/° C

platinum       9.0 E - 6/° C            benzene            1.24 E - 3/° C

glass            9.0 E - 6/° C                mercury            1.8 E - 4/° C

steel            2.0 E – 5/°C                water                 2.1 E – 5/°C  

 

Answers available from Mr. Jones