energy of the particles in a system; this occurs during a phase change. Heat is required to melt
something (change its phase from solid to liquid) or to vaporize something (change its phase from
liquid to gas). In both cases (and also in the case of sublimation, where a solid is converted into a gas
directly), the molecules are overcoming the attractive forces that hold them together. This is where
the energy supplied by heating is being “put to use.” Conversely, heat is released as a substance
crystallizes (or freezes) or condenses. During such phase changes the temperature remains
constant, and the heat involved in these processes can be expressed as:
q = mLwhere m is again the mass of the substance undergoing the phase change and L is the heat of
transformation, the value of which depends on both the substance and the particular process we
are talking about: vaporization, sublimation, fusion (melting), et cetera.
The heats of transformation for two reverse processes have the same magnitude; that is, the heat of
fusion is the same as the heat of crystallization with opposite sign; the heat of vaporization is the
same as the heat of condensation with opposite sign; and so forth.
To bring a cube of ice at −50°C to water vapor at 130°C, then, the heat required would be:
q = mcice (50°C) + mLfus + mcwater (100°C) + mLvap + mcsteam (30°C)where Lfus is the heat of fusion of water and Lvap the heat of vaporization of water. Only one m value
is needed since mass is conserved.
The “heating curve,” a plot of the temperature versus the amount of heat added, would look like: