Page 239 - Schaum's Outline of Theory and Problems of Applied Physics

CHAPTER 19

Expansion of Solids,

Liquids, and Gases

LINEAR EXPANSION

A change in temperature T causes most solids to change in length (or other linear dimension) by an amount
L that is proportional to both the original length L 0 and T :

L = aL 0 T
Change in length = (a)(original length)(temperature change)

The quantity a is a constant that depends on the nature of the material; it is called the coefficient of linear
expansion.

VOLUMEEXPANSION
The change in volume V of a solid or liquid whose original volume is V 0 when its temperature is changed by
T is
V = bV 0 T

Change in volume = (b)(original volume)(temperature change)
The quantity b is the coefficient of volume expansion. Generally b = 3a for a given material.

SOLVED PROBLEM 19.1

A surveyor’s steel tape measure is calibrated at 20 C. A reading of 50 m is found when the tape measure
◦
is used to determine the width of a building lot when the temperature is −10 C. How great an error does
◦
the temperature difference introduce? The coefficient of linear expansion of steel is 1.2 × 10 / C.
−5 ◦
◦
◦
Since T = 20 C − (−10 C) = 30 C, the 50-m length of steel tape shrinks by
◦
◦
−5 ◦
L = aL 0 T = (1.2 × 10 / C)(50 m)(30 C) = 1.8 × 10 −2 m = 18 mm
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