freeze at the top first. As a lake cools toward ° C, water near the surface loses energy to the atmosphere, becomes denser, and sinks; the warmer, less dense water near the bottom rises. However, once the colder water on top reaches temperature below ° C, it becomes less dense and remains at the surface, where it freezes. If water did not have this property, lakes and ponds would freeze from the bottom up, which would destroy much of their animal and plant life.
Gases, at ordinary temperature, expand more than solids and liquids. For liquids, the coefficient of volume expansion is relatively independent of the temperature. However, for gases it is dependent on temperature. For an ideal gas, the coefficient of volume expansion at constant pressure can be found from the ideal gas equation: PV = µ RT At constant pressure P ∆ V = µ R ∆ T i.e., α v = for ideal gas ( .
) At ° C, α v = . × – K – , which is much larger than that for solids and liquids. Equation ( . ) shows the temperature dependence of α v ; it decreases with increasing temperature.
For a gas at room temperature and constant pressure, α v is about × – K – , as Temperature ( ° C) Temperature ( ° C) (a) (b) Fig. . Thermal expansion of water. much as order(s) of magnitude larger than the coefficient of volume expansion of typical liquids.
There is a simple relation between the coefficient of volume expansion ( α v ) and coefficient of linear expansion ( α l ). Imagine a cube of length, l , that expands equally in all directions, when its temperature increases by ∆ T . We have ∆ l = α l l ∆ T so, ∆ V = ( l+ ∆ l ) – l ≃ l ∆ l ( . ) In Equation ( .
), terms in ( ∆ l ) and ( ∆ l ) have been neglected since ∆ l