Graphing Entropy

Last time we saw that chemists can calculate the entropy of any substance at any temperature

For instance, the entropy of a mole of water at this temperature [263K] is this [39.9 J K^–1 mol^-1].

At this temperature, it’s this [298K – 69.9 J K^–1 mol^-1]

And at this temperature [373K] it’s this [202.5 J K^–1 mol^-1]

Now, if we continued charting the entropy of water at different temperatures we’d end up with a graph like this 

This graph shows exactly how the entropy of water varies with temperature. 

And in this lesson, we’re going to investigate its unique shape using what we already know about entropy.

First, the graph starts at the origin…

And that makes sense because, as we’ve seen before, the entropy of any substance at zero kelvin is zero

Next, as the temperature rises from 0 to 273K entropy increases steadily. 

And that makes sense because, as we’ve seen before, when temperature increases, entropy increases.

Next we get to 273K, or 0^oC, and the entropy jumps up sharply and significantly

And that makes sense because 273K is the point at which water turns from solid to liquid. 

And, as we’ve seen before, liquids are much more disordered than solids. 

So that means, at water’s melting point, a tiny increase in temperature results in a large jump in entropy. 

Next up, from 273K to 373K entropy increases steadily again

And that makes sense because when temperature increases, entropy increases.

Then we reach 373K, or 100^oC, and entropy shoots up again…

And that makes sense because 373K is the point at which water turns from a liquid into a gas. 

And, as we’ve seen before, gases are much more disordered than liquids. 

So that means, at water’s boiling point, a tiny increase in temperature results in a huge jump in entropy. 

Even larger than the jump here… 

And that makes sense because there’s a larger increase in disorder when a substance turns from liquid to gas… than there is when that substance turns from solid to liquid. 

Lastly, from 373K onwards, entropy increases steadily again. 

So, we’ve now analysed every aspect of this graph which charts water’s entropy at different temperatures.

…But water isn’t the only substance with a graph like this.

For example, here’s the graph for diatomic nitrogen, and here’s the graph for aluminium

And we can interpret these just like we did the one for water

So, using this graph, what’s the boiling point of aluminium? 

The boiling point of aluminium is 2743 kelvin, since that’s where the second large jump takes place

And, using this graph, what’s the entropy of a mole of nitrogen at 298K?

The entropy of a mole of nitrogen at 298K is 191 joules per kelvin

So, to sum up…

For any substance, chemists can make a graph of how its entropy changes with temperature. 

And these graphs.

These graphs start at the origin, show that entropy increases with temperature, and have large jumps at the melting and boiling points of the substance where the boiling point jump is larger than the melting point jump.