Phase Changes

The specific heat capacity is used in calculations where a given substance is heated from one temperature to another. The input heat results in a higher temperature of the substance. As long as the substance doesn't change its physical phase this works. All bets are off on this premise when there is a phase change.

There are 3 normal phases of matter that we are concerned with - solid, liquid, and gas. Each phase can directly change into the others and vice versa, therefore there are a total of 6 possible changes. Really this is 3 changes with 2 directions of change possible in each. The illustration below show this.

Note that each change has an associated name and that half of them are endothermic (the red arrows) and the other half are exothermic (the blue arrows). Each change occurs at a specific temperature as well. Let's look at each change and get the lingo down as well as the sign convention.


The temperature for melting a solid to a liquid is the melting temperature which is identical to the freezing temperature where you go the other way from liquid to solid. As and example, water has a freezing temperature of 0 °C (32 °F) and ice has a melting temperature of 0 °C (32 °F). Melting is also known as fusion and the heat required to melt a specific amount of substance is the heat or enthalpy of fusion which is symbolized as ΔHfus and it is a positive (+) quantity - meaning you ADD heat to the solid (endothermic) to get it to melt to the liquid state. Going the opposite way is freezing and the heat/enthalpy of freezing is a negative quantity (exothermic) because heat is removed or released. The heat of fusion of water is 334 J/g.


The temperature at this transition is the boiling point (liquid to gas) or the condensation point (gas to liquid). Remember, it is the same temperature either way. For water, the boiling point is 100 °C (212 °F). The amount of heat to cause this change is the heat of vaporization or ΔHvap and it is a positive quantity (endothermic). Water has a heat of vaporization of 2260 J/g. The heat of condensation is just the negative (exothermic) of that value.


The temperature of the transition is the sublimation point (solid to gas). The heat required for the transition is the heat/enthalpy of sublimation, ΔHsub.

There is no ΔT in the Calculation

ALL these transitions occur at the transition temperature and there is no change in temperature throughout the transition. So the calculation of the heat required just needs the ΔH value and the amount of substance.

qtrans = mtrans·ΔHtrans

Where the "trans" is for which ever transition you are calculating for. For example, if I want to calculate the amount of heat that will melt 25 grams of ice at 0 °C into 25 grams of water at 0 °C, I'd do the following.

qfusion = (25 g)(334 J/g)

qfusion = 8350 J

And, just like with heat capacities, you can also have heats of transitions in terms of moles instead of grams. So always double check the units that your are given - you might have to convert from moles to grams or vice versa.

There is a TABLE of Phase Change Data in the Appendix

There is a table of phase change data (melting point, heat of fusion, boiling point, heat of vaporization) in the Appendix (Section 10.09). There are numberous substances listed. Look there for data for homework problems.

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