1.5 Phase changes  (Page 4/20)

Where does the heat added during melting or boiling go, considering that the temperature does not change until the transition is complete? Energy is required to melt a solid, because the attractive forces between the molecules in the solid must be broken apart, so that in the liquid, the molecules can move around at comparable kinetic energies; thus, there is no rise in temperature. Energy is needed to vaporize a liquid for similar reasons. Conversely, work is done by attractive forces when molecules are brought together during freezing and condensation. That energy must be transferred out of the system, usually in the form of heat, to allow the molecules to stay together ( [link] ). Thus, condensation occurs in association with cold objects—the glass in [link] , for example.

The energy released when a liquid freezes is used by orange growers when the temperature approaches $0\text{°}\text{C}$ . Growers spray water on the trees so that the water freezes and heat is released to the growing oranges. This prevents the temperature inside the orange from dropping below freezing, which would damage the fruit ( [link] ).

The energy involved in a phase change depends on the number of bonds or force pairs and their strength. The number of bonds is proportional to the number of molecules and thus to the mass of the sample. The energy per unit mass required to change a substance from the solid phase to the liquid phase, or released when the substance changes from liquid to solid, is known as the heat of fusion    . The energy per unit mass required to change a substance from the liquid phase to the vapor phase is known as the heat of vaporization    . The strength of the forces depends on the type of molecules. The heat Q absorbed or released in a phase change in a sample of mass m is given by

where the latent heat of fusion $L_{\text{f}}$ and latent heat of vaporization $L_{\text{v}}$ are material constants that are determined experimentally. (Latent heats are also called latent heat coefficient     s and heats of transformation.) These constants are “latent,” or hidden, because in phase changes, energy enters or leaves a system without causing a temperature change in the system, so in effect, the energy is hidden.