\(\def \u#1{\,\mathrm{#1}}\) \(\def \abs#1{\left|#1\right|}\) \(\def \ast{*}\) \(\def \deg{^{\circ}}\) \(\def \tau{\uptau}\) \(\def \ten#1{\times 10^{#1}}\) \(\def \redcancel#1{{\color{red}\cancel{#1}}}\) \(\def \BLUE#1{{\color{blue} #1}}\) \(\def \RED#1{{\color{red} #1}}\) \(\def \PURPLE#1{{\color{purple} #1}}\) \(\def \th#1,#2{#1,\!#2}\) \(\def \lshift#1#2{\underset{\Leftarrow\atop{#2}}#1}}\) \(\def \rshift#1#2{\underset{\Rightarrow\atop{#2}}#1}}\) \(\def \dotspot{{\color{lightgray}{\circ}}}\) \(\def \ccw{\circlearrowleft}\) \(\def \cw{\circlearrowright}\)
Chapter 7: Thermodynamics
4.

Phase Changes

Materials can exist in one of three phases, depending on their temperature: as solids, liquids, or gases. (You are probably familiar with these already, but we discuss these more in What is a Fluid?). When a solid is warmed above its melting (or freezing) temperature it changes into a liquid, and when it is warmed above its boiling temperature, it changes again into a gas. (Some materials, such as carbon dioxide at standard atmospheric pressure, will change directly from a solid to a gas at a sublimation temperature). Above the melting temperature, the solid phase is unstable, while below it the liquid phase is unstable. Only when the temperature is at the melting point can the two phases coexist at once: therefore a cup of ice water can only survive as ice water at 0°C, the melting point of water.

You might think that ice and liquid water at 0°C would have the same thermal energy, but in fact liquids have an additional amount of energy, called latent energy or latent heat (a terrible name, but the more common one), that solids do not; and gases have yet an additional amount of latent energy that liquids do not. Thus to melt ice, it isn't enough to raise its temperature to 0°C, you must also provide it with enough additional energy (usually as heat) to change it into a liquid. The reverse is true as well: for liquid water to freeze it must shed its latent energy into the environment.

Latent Energy
\(E_L\)
J
Latent Energy per kg
\(L\)
J/kg
The latent energy $E_L$ of a phase depends both on its mass and the type of material it is, and is given by the formula

$$E_L=mL$$

Note

Imagine that you placed a large number of 0° ice cubes into a cup of water at room temperature. Because the ice is colder than the water, heat will flow out of the water into the ice. This flow of heat will cool the water, but it will not warm up the ice: rather the heat will be used to melt some of the ice, turning it into liquid water, at which point it can then start to warm up as usual. If there is enough ice, it might absorb the room temperature water's thermal energy to the point where the water is now at 0°C, at which point no more heat will flow because the system is in thermal equilibrium. This is why ice is so useful in cooling things, much more useful than very cold water, because it can absorb heat without changing temperature during the melting process.

Something similar happens during evaporation, which is when liquid water turns into water vapor. When we sweat, for instance, the liquid water on our skin absorbs heat from our body in the process of turning into water vapor, thus cooling us off. (This can occur at temperatures below 100°C because evaporation is a surface effect, rather than a bulk effect. When a container of water is below the boiling point, water molecules can still escape from the surface into the air. But once it reaches the boiling point, all of the water turns into steam at once, not just the water at the surface. The concept of latent energy still applies in both cases, however.)