18.11 - Thermal expansion: volume

Thermal volume expansion:

Change in volume due to a

change in temperature.

The equation for thermal linear expansion is used to

calculate the thermally induced change in the size of

an object in just one dimension. Thermal expansion

or contraction also changes the volume of a material,

and for liquids (and many solids) it is more useful to

determine the change in volume rather than expansion along one dimension. The

expansion in volume can be significant. Automobile cooling systems have tanks that

capture excess coolant when the heated fluid expands so much it exceeds the

radiator’s capacity. A radiator and its overflow tank are shown in Concept 1 on the right.

The formula in Equation 1 resembles that for linear expansion: The increase is

proportional to the initial volume, a constant, and the change in temperature. The

constant ȕ is called the coefficient of volume expansion.

Above, you see a table of coefficients of volume expansion for some liquids and solids.

The coefficients for liquids are valid for temperatures at which these substances remain

liquid.

For solid materials like copper and lead, the coefficient of volume expansion ȕ is about

three times the coefficient of linear expansion Į, because the solid expands linearly in

three dimensions.

Thermal expansion: volume

Volume increases with temperature

Constant ȕ varies by material

Increase is proportional to initial volume

ǻV = ViȕǻT

V = volume

ȕ = coefficient of volume expansion

ǻT = change in temperature

Coefficient calibrated for K or °C

For solids

ȕ§ 3 Į

ȕ = coefficient of volume expansion

Į = coefficient of linear expansion

(^342) Copyright 2007 Kinetic Books Co. Chapter 18