When materials change temperature they can change state, this is called a phase change. The obvious examples are melting, vaporisation, condensing and freezing (solidifying). There are also the less obvious subliming and resubliming (changing directly from solid to gas and back again) together with phase changes that can occur in a solid at different temperatures and pressures (there are for example more than a dozen different types of frozen water, although only two can exist outside a laboratory on Earth).
Whenever there is a phase change (change of state) in a material, the atoms or molecules involved are rearranged. This usually involves a change of energy which can be seen as the latent heat (of fusion or vaporisation etc.). After the phase change the rearranged atoms will respond to a change in energy differently and so the specific heat capacity is also likely to change. In addition the rearrangement may well mean a change in the way the atoms are packed together and so a change in density is also very common.
If you used the worksheet “Chilling Tales” you would have looked at cooling curves whilst the material is in a single phase. If a phase change is involved then the graph will be a different shape. This is the shape of the curve if the material is a pure substance such as water, ethanol or mercury.
And if the substance is a mixture, such as candle wax the curve will look slightly different.
The energy that is lost from the object during solidification is called the Latent Heat of Fusion. If the object has a unit mass (usually a kilogram) then the term Specific Latent Heart of Fusion is used. Latent heat (both of fusion and its liquid to gas equivalent the Latent Heat of Vaporization) are important in many situations:
Many animals, including humans, prevent overheating by allowing water in the form of sweat or saliva to evaporate, carrying excess heat away with it (if you are too hot, fan the sweat away from your forehead, don’t wipe it off).
Reusable ‘hand comforters’ and baby’s bottle warmers work by cooling a liquid below its melting point. Clicking a metal disc triggers crystal formation that rapidly spreads through the entire pack. This releases the latent heat of fusion and warms your hands.
Metallurgists need to know about the specific latent heat of fusion because before a casting can be made or an alloy mixed the metals involved must be melted. The cost of the energy to do this can be a significant part of the total cost. Additionally the heat that needs to be removed from the casting before it is solidified will affect how the process progresses and so affect the grain structure of the final casting.
There are many methods that can be used to do this and the best one for the purpose will depend in part on the materials being tested. The method for measuring the latent heat of fusion of ice would not work very well for iron or aluminium. Here are two different specific latent heat experiments for you to carry out.
This method works well for ice as well as other chemicals with a melting point at a little below room temperature.
Experimental Setup with Power Circuit
The two set ups should be identical other than the fact that the control is not connected to a power supply.:
Place the two immersion heaters in the funnels and pack the crushed ice around them. The element of the heaters should be positioned towards the end of the metal barrel; check that this is in good contact with the ice. Connect one heater to the power supply but do not turn it on.
Record the weights of the two beakers and place them under the funnels.
Wait until both funnels are dripping water into their beakers then turn on the power supply and at the same time start the stop clock.
Record the current and potential difference of the supply circuit and do not alter it (if data logging equipment is available the values can be constantly tracked and the resultant power and energy delivered calculated automatically).
Ensure that the ice is kept topped up and in good contact with the two heaters.
The ideal duration of the experiment will depend on several factors including the power of the heater, the size of the funnel and room temperature etc. However as a guide, a duration of five minutes should be adequate.
Turn off the power and stop the clock but do not move the beakers.
After another minute or so (when the flow of melt water is back to the rate of the control setup) remove the beakers and weigh them again.
Calculate the weight of water deposited in each beaker. Subtract the weight of water in the control beaker from that in the experimental beaker. This mass, , is equal to the weight of ice melted due solely to the effect of the heater.
This method works well for substances with a melting point at a modest distance above room temperature. Chemicals such as stearic or lauric acid are ideal.
Experimental Setup with Power Circuit
Weigh the insulated beaker.
Measure out sufficient of the test material to well cover the element of the immersion heater when it is placed in the insulated beaker. Weigh the measuring beaker with it contents.
Turn on the heater and fully melt the test solid so that the heater and temperature probe can be put in place and fixed with clamps. Allow the material to resolidify and record the temperature at regular intervals.
Allow the material to cool a few degrees below the melting point. Turn on the heater and record the current and potential difference readings.
Record the temperature at regular intervals until the material is a few degrees above the melting point.
Repeat the previous two steps several times but with a different settings for the power supply.
The latent heat of fusion of the sample is given by:
Where L is the specific latent heat of fusion and is the mass of the sample. If we divide by time we have the power , that is going solely into melting the sample.
But the total power supplied is divided between this and the rate of heat loss to the surroundings :
Writing this out in full we can put the equation into form:
So if we draw a graph of total power against the inverse of the melting time we should produce a straight line graph with a y intercept of the rate of heat loss to the surroundings and a gradient of the specific heat capacity multiplied by the mass of the sample.
There is one additional point that can be added to the graph as the x intercept corresponds to zero total power and the relevant time is therefore the time it took the sample to solidify when the power had been turned off.
In practice methods 1 & 2 would be too slow and prone to error. A typical commercial laboratory would carry out many tests on similar materials and so would require a method that was both quick, automatic and reliable. Ideally a dedicated piece of equipment would be purchased so that results would be easily repeated and measurements calibrated. A (relatively) simple method has been developed that lends itself to this automation; it is called ‘differential scanning calorimetry’.
The technique works as follows:
Two samples are prepared, the one to be investigated and a reference sample with a well known heat capacity over the temperature range to be studied.
The two samples are loaded into the differential scanning calorimeter where they are both heated.
The amount of heat energy delivered to the reference sample is calculated so that its temperature closely matches the sample to be analysed.
At the end of the run the difference between the heat energy delivered to the two samples is solely due to the thermal characteristics of the sample under test.