Heating Ice into Steam - avoiding mistakes on the graph

This crops up when teaching solids, liquids and gases and changes of state. In particular, the (idealised) graph of Temperature against time you get when you heat a solid (ice is the usual example) until it melts, then continue heating it until it boils and is entirely a gas. It is sometimes shown accurately in books, but I've seen it done very badly too. By the usual quick check of doing a Google image search, it looks to me like nearly 50% of the offerings out there (often the hand-drawn ones) are either slightly or very incorrect.

First of all, here is a correct version, based on actual calculations and assuming a constant power input:


Here are some of things that often seem to be shown incorrectly:

  • The gradients of the three heating sections (where the temperature is rising) will not be the same. You can show that the gradient of these sections of the graph will be inversely proportional to the specific heat capacity of the substance in that state. In the case of water, the SHC of liquid water is about double those of ice and steam, hence the gradient of the middle heating section, above, is about half the gradients of the other two. This isn't easy to see, though, due to the x-axis scale.

[Actually, the heating sections wouldn't be perfectly straight because SHCs do vary slightly with temperature, but it wouldn't be noticeable on this scale]

  • The time it takes for a change of state to occur will be proportional to the specific latent heat of the substance for that change. Since SLHs of vaporisation are usually about 10 times bigger than the same substance's SLH of fusion, the second change of state should take about 10 times longer than the first.


Of course, both of these statements assume the power input is constant. If it isn't, then the graph could have almost any proportions you wanted.

It is also worth stressing that getting a perfect graph like that in practice is nigh-impossible. A lack of perfect insulation will be the first thing to muck up the graph, not to mention the fact that thermal energy losses will change as the temperature difference between the substance and its surroundings changes.


Having said all of that, though, I would say that it is a worthwhile thing for pupils to know, as long as its limitations are clear.