Engineering Fundamentals: An Introduction to Engineering, 4th ed.c

332 Chapter 11 Temperature and Temperature-Related Parameters

Note that the coefficient of linear expansion is a property of a material and has the units of

1/F or 1/C. Because a 1Fahrenheit temperature difference is equal to a 1Rankine temper-

ature difference, and a 1Celsius temperature difference is equal to a 1 Kelvin temperature dif-

ference, the units of aLcan also be expressed using 1/R and 1/K. The values of the coefficient

of linear expansion itself depend on temperature; however, average values may be used for a

specific temperature range. The values of the coefficient of thermal expansion for various solid

materials for a temperature range of 0C to 100C are given in Table 11.10. Equation (11.24)

could be expressed in such a way as to allow for direct calculation of the change in the length

that occurs due to temperature change in the following manner:

(11.25)

For liquids and gases, in place of the coefficient of linear expansion, it is customary to

define the coefficient of volumetric thermal expansion, aV. The coefficient of volumetric expan-

sion is defined as the change in the volume, ¢V, per original volumeVper degree rise in tem-

perature, ¢T, and is given by the following relationship:

(11.26)

Note that the coefficient of volumetric expansion also has the units of 1/F or 1/C. Equa-

tion (11.26) could also be used for solids. Moreover, for homogeneous solid materials, the

relationship between the coefficient of linear expansion and the coefficient of volumetric expan-

sion is given by

aV 3 aL (11.27)

aV

¢V

V ¢T

¢LaLL ¢T

TABLE 11.10 The Coefficients of Linear Thermal Expansion for Various Solid Materials

(mean value over 0 C to 100 C or 32 F to 212 F)

Solid Material Mean Value of aaL(1/F) Mean Value of aaL(1/C)

Brick 5.3 10

 6

2.9 10

 6

Bronze 10.0 10

 6

5.5 10

 6

Cast iron 5.9 10

 6

3.3 10

 6

Concrete 8.0 10

 6

4.4 10

 6

Glass (plate) 5.0 10

 6

2.8 10

 6

Glass (Pyrex) 1.8 10

 6

1.0 10

 6

Glass (thermometer) 4.5 10

 6

2.5 10

 6

Masonry 2.5 10

 6

–5.0 10

 6

1.4 10

 6

• 2.8 10

 6

Solder 13.4 10

 6

7.4 10

 6

Stainless steel (AISI 316) 2.9 10

 6

1.6 10

 6

Steel (hard-rolled) 5.6 10

 6

3.1 10

 6

Steel (soft-rolled) 6.3 10

 6

3.5 10

 6

Wood (oak) normal to fiber 3.0 10

 6

1.7 10

 6

Wood (oak) parallel to fiber 2.7 10

 6

1.5 10

 6

Wood (pine) parallel to fiber 3.0 10

 6

1.7 10

 6

°°°°

Source:T. Baumeister,et al., Mark’s Handbook.

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀