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.

Melting/Freezing

The temperature at which a solid melts to become a liquid is known as the melting point (mp) which is identical numerically to the freezing point (fp). When you say freezing point, you are inferring that the liquid is freezing into a solid. As an example, water has a freezing point of 0 °C (32 °F) and ice has a melting point 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 ΔH_fus 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.

Vaporization/Condensation

The temperature at the liquid/gas transition is the boiling point (bp) or the condensation point (rarely referred to BTW). 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 ΔH_vap 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. Also important here... notice how much bigger (almost 7×) the heat of vaporization is compared to the heat of fusion. This is because you must overcome ALL the IMFs of the substance to transition to gas phase.

Sublimation/Deposition

The temperature of the transition is the sublimation point (solid to gas). The heat required for the transition is the heat/enthalpy of sublimation, ΔH_sub. The value (under standard conditions) of the heat of sublimation of a substance is equal to the sum of the heats of fusion and vaporization (ΔH_sub = ΔH_fus + ΔH_vap ).

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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. The "amount" can be mass in grams or amount in moles. Be sure and check the units on your ΔH value to see which amount you need to use: grams or moles. Here is the equation using mass (m).

q_trans = m_trans·ΔH_trans

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.

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

q_fusion = 8350 J

And to reiterate, 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.

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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.