Reconciliation of the Language of Thermal Expansion
Thermal expansion is the increase in the length, or
volume of a body during heating. The coefficient of linear thermal
expansion is the relative elongation with rise in temperature of one degree.
A centimeter length of copper increases
approximately 0.0000167 centimeters with a rise of one degree centigrade.
This figure varies slightly from one observer to another.
An inch length of copper increases approximately
0.0000167 inches with a rise of one degree centigrade. The unit of length
is immaterial.
A centimeter length of copper increases
approximately 0.0000093 centimeters with a rise of one degree Fahrenheit.
The increment of temperature is material. One degree centigrade equals
9/5 of a degree Fahrenheit. Or, 0.0000093 x 9/5 = 0.0000167.
The change in volume can be assumed with sufficient
accuracy to be three times the change in length. Thus, one cubic
centimeter of copper increases approximately 0.0000501 cubic centimeters with a
rise of one degree centigrade. Or, 0.0000167 x 3 = 0.0000501.
Metallurgists think in terms of linear thermal
expansion as in./in./ºF. To them, copper has a coefficient of linear
thermal expansion of 0.0000093 in./in./ºF.
Glass workers also think in terms of linear thermal
expansion, but as cm/cm/ºC. To them, copper has a coefficient of linear
thermal expansion of 0.0000167 cm/cm/ºC.
Enamelers think in terms of volume thermal
expansion as cm/cm/ºC. To them, copper has a coefficient of volume
thermal expansion of 0.0000501 cm/cm/ºC.
Mathematicians have taught us how to eliminate
decimals:
10 
= 
10^{1} 
1 
= 
10^{0} 
.1 
= 
10^{1} 
.01 
= 
10^{2} 
.001 
= 
10^{3} 
.0001 
= 
10^{4} 
.00001 
= 
10^{5} 
.000001 
= 
10^{6} 
.0000001 
= 
10^{7} 
Multiplying 501 by .0000001 we obtain 0.0000501 or
501 x 10^{7} = 0.0000501 or 0.0000501 = 501 x 10^{7}.
Thus, enamelers say the coefficient of volume
expansion of copper is 501 cm/cm/ºC x 10^{7}.
(This may be the origin of the old saying, "Improved to death".)
Glass workers multiply 167 by .0000001 and obtain
.0000167. They say the coefficient of linear thermal expansion of copper
is 167 cm/cm/ºC x 10^{7}.
However, Metallurgists are different. Perhaps
they do not like negative exponents. Mathematicians also teach that:
10 
= 
10^{1} 
100 
= 
10^{2} 
1000 
= 
10^{3} 
10,000 
= 
10^{4} 
100,000 
= 
10^{5} 
1,000,000 
= 
10^{6} 
Metallurgists multiply 0.0000093 times 1,000,000
and obtain 9.3. They say the coefficient of linear thermal expansion of
copper times 10^{6} is 9.3 in./in./ºF.
