absorbed. The change in volume, ∆V, corresponding to a temperature change, ∆T,
is given by the equation
∆V = βV 0 ∆Twhere V 0 is the sample’s initial volume and β is the coefficient of volume
expansion of the substance. Since we’re now looking at the change in a three-
dimensional quantity (volume) rather than a one-dimensional quantity (length), for
most solids, β ≈ 3α. Nearly all substances have a positive value of β, which means
they expand upon heating. An extremely important example of a substance with a
negative value of β is liquid water between 0°C and 4°C. Unlike the vast majority
of substances, liquid water expands as it nears its freezing point and solidifies
(which is why ice has a lower density and floats in water).
- The mercury in a household glass-tube thermometer has a
volume of 500 mm^3 (= 5.0 × 10−7 m^3 ) at T = 19°C. The hollow
column within which the mercury can rise or fall has a cross-
sectional area of 0.1 mm^2 (= 1.0 × 10−7 m^2 ). Ignoring the volume
expansion of the glass, how much will the mercury rise in the
thermometer when its temperature is 39°C? (The coefficient of
volume expansion of mercury is 1.8 × 10−4/°C.)
Here’s How to Crack It
First let’s figure out by how much the volume of the mercury increases.
∆V = βV 0 ∆T = (5.0 × 10−7 m^3 )(39°C−19°C) = 1.8 × 10−9 m^3Now, since volume = cross-sectional area × height, the change in height of the
mercury column will be
∆h = = = 1.8 × 10−2 m = 1.8 cm