Most (but not all!) objects tend to expand when heated – that is, their dimensions increase.  This property of solids and liquids is called thermal  expansion.  There are two types of thermal expansion that we will be considering: the linear expansion of one dimension of an object, and the volume expansion of solids and liquids.

Linear Expansion

If an object has an initial length L_i at a temperature T_i, and a final length L_f at a temperature T_f , then the change in length of the object, DL = L_f – L_i , is given by

DL = aL_iDT ,

where DT = T_f – T_i is the change in temperature of the object, and a (Greek letter alpha) is a constant which is characteristic of the material of which the object is made, called  the coefficient of linear expansion.  We can see from the equation above that a must have the units of 1/C^o or 1/K. (Note that we use the symbol “C^o”, Celsius degrees, to denote a change in temperature, while we use “^oC”, degrees Celsius,  to denote the units of a temperature reading.)  The table below gives some characteristic values of the expansion coefficient a.

Volume Expansion

Volume expansion works almost identically to linear expansion. If an object or substance of initial volume V_i undergoes a change in temperature DT, then its volume will change by an amount

DV = bV_iDT .

The constant b is called the coefficient of volume expansion.  Some values of b are given in the table below.

In some solids, the value of a is the same no matter which direction in the  solid we are talking about.  For example, the value of a does not depend on  whether we are talking about the length or the width of the solid object. Such an object is called an isotropic solid.  In this case, the volume expansion coefficient b is simply given by

b = 3a .   (Isotropic solid)

Unless stated otherwise, we shall assume that any solid material that we are working with can be treated as an isotropic solid.