### Episode 608: Latent heat

Energy is involved in changes of phase, even though there is no change of temperature.

 SummaryDiscussion: Defining specific latent heat. (10 minutes)Demonstration: Boiling water. (15 minutes)Student experiment: Measuring l. (30 minutes)Student experiment: Cooling curves. (30 minutes)Worked example: Latent and specific heat (5 minutes)Student questions: Involving c and l. (40 minutes)

Discussion: Defining specific latent heat
The final point in this topic is to return to the original definition of internal energy as being both kinetic and potential. In talking about ideal gases all the energy was kinetic because there were assumed to be no bonds between the atoms. However, in a solid or liquid there are bonds and clearly some energy is needed to break those bonds. That means that, in melting a solid or boiling a liquid, a substantial amount more energy needs to be added which does not raise the temperature. This is the latent (“hidden”) heat.

The energy required to melt a mass m of a substance is given by

ΔE = ml.

Or the specific latent heat is the energy required to change the unit mass from one phase to another.

Demonstration: Boiling water
Ask your class to watch some water boiling and think about what is going on. Energy is being supplied, but the temperature is not rising. The energy is breaking intermolecular bonds, or, as a physicist would say, work is being done to separate the particles against intermolecular attractive forces.

The key point from these is that, for certain materials, there is a phase transition where the heat energy no longer raises the temperature (kinetic energy per molecule) but instead breaks bonds and separates the particles (potential energy). This should be made quantitative. Likewise, the reverse processes involve energy being given up from the substance. So evaporating liquids are good coolants and freezing water to make ice is considerably more of an effort than cooling water to 0 °C.

TAP 608-1: Examination of boiling

Student experiment: Measuring L
It is useful to have measured a specific latent heat – for example, that of melting ice.

TAP 608-2: The specific latent heat of fusion of ice

Student experiment: Cooling curves
If you have a class set of data-loggers for recording temperature, determination of the cooling curve of stearic acid, naphthalene or lauric acid is worthwhile. Even as a demonstration this is good and can be left running in the background while the students work on calculations.

TAP 608-3: Heating and cooling curves

Worked example: Latent and specific heat
Scalds from water and steam

We assume that our hand is at 37 oC, and that we put 10 g of water at 100 oC accidentally on our hand. The water will cool to 37 oC. Assuming that all the heat energy "lost" by the water will be gained by our hand:

Heat "lost" by water = m c Dθ = 0.01 x 4200 x 63 =2,646 J.

But if the 10 g had been steam then the steam would first have to condense.

Heat "lost" in condensing = ml = 0.01 x 2260000 = 22,600 J

So the heat lost in 10 g of steam turning to water at 37 oC is 22,600 + 2,646 = 25,246 J.

This is nearly ten times as much as the water alone!

The worked example is based on one from Resourceful Physics.

Student questions: Involving c and l
Practice in situations involving specific heat capacity and specific latent heat.

TAP 608-4: Questions involving specific heat capacity and specific latent heat

TAP 608-5: Further specific and latent heat questions