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Red-Hot Steel vs. Frozen Lake: A Real-World Energy Problem

Robert Prior, ePublisher of OAPT Newsletter

What happens when you heat a 20 kg cylinder of steel red-hot, and put it on a frozen lake? This may look like a silly question, but Lauri and Anni Vuohensilta — the crazy Finns of Beyond the Press — did it, and it makes a nice guided inquiry activity for exploring energy transfer in the grade 11 physics.

Calculating accurate energy transfer during phase changes is both too simple and too complicated for our students. Too simple because most textbook problems are just three-variable, plug-n-chug questions with no thinking needed; too complicated because a full analytical solution requires skills beyond the high-school level.

Ever since I found this video on YouTube, I’ve used it as a guided inquiry activity to walk students through the process of making approximations to analyze real-world events. Here is an overview of the lesson.

I set the scene by playing the first 90 seconds of the video. Then I pause it, and ask the students to write their answers to Lauri’s question: “What will happen when he places the red-hot steel on the ice?”. Once they have their answers, they want to see the rest of the video. I tell them that first they must back up their answer with calculations. I insist that they understand more than they realize.

Energy Flows
The first thing to do is figure out what is happening. Where is energy flowing? What is it doing? Are there flows that we can ignore? Are there flows that we can’t calculate, so must omit from a numerical analysis?

They discuss these questions in their groups*, then we see if we have a class consensus. We end up with the following points (some classes need more prodding than others):
  • thermal energy is leaving the steel, which is cooling down
  • thermal energy is entering the air from the steel, which is warming up
  • thermal energy is entering the ice, which is warming up
  • thermal energy is entering the ice, which is melting
  • thermal energy is entering the water (melted ice), warming it up
  • thermal energy is entering the water (melted ice), evaporating it
  • thermal energy is leaving the warm water, melting more ice and heating more air
  • all the above will happen until the steel and ice/water/air are at the same temperature
This looks complicated, but an energy flow diagram usually helps clarify things for students.

The steel cylinder will sink into the ice, melting both the bottom of the hole (where it contacts the ice) and the sides (by warming water, that in turn melts more ice), so we are in effect melting an inverted, truncated cone. If the height of the cone is more than the thickness of the ice, it will fall through.

Assumptions and Simplifications
So what assumptions and simplifications will we need to make, in order to do a quantitative analysis? Time for the class to break into their groups again, and see what they come up with.

After more group discussions, we (hopefully) have the following simplifications. Sometimes I have to prod/lead more than others.

We can’t calculate the thermal energy that warms the air, so we’ll have to leave it out of our calculations. Air has a low mass, though, so a quick back-of-the-envelope calculation shows we’re safe in ignoring it.

The hot water will cool down as it melts more ice, eventually reaching thermal equilibrium back at 0°, so as a simplification we can ignore heating the water and just calculate the energy for melting the ice.

We don’t know the initial temperature of the ice, but it is floating on water, so is likely very close to 0°. The energy required to change the temperature of ice by a couple of degrees is much less than that required to melt it, so as a simplification we can assume that the ice starts at 0°.

At this point we have simplified the problem to, “How much ice can 20 kg of red-hot steel melt?” We also know that our solution will be an overestimate.

We know how wide the bottom of the cone is (the diameter of the steel cylinder), but can we calculate how wide the top is? Not really, so another simplification: assume that the ice melted is a cylinder of the same diameter as the steel. This will overestimate the depth of the hole the steel will melt.

So our final problem is “what is the height of the cylinder of ice melted by 20 kg of red-hot steel?”

Sometimes groups make different assumptions — for example, assuming that there will be a 2 cm gap at the top of the hole — so they end up with slightly different calculations. This is great because they are thinking for themselves.

Initial Conditions
We watch the beginning of the video again, noting any information given. The students all get the data that the Vuohensiltas put on the screen: 20 kg of steel, 30 cm thick ice. Most catch the diameter of the steel cylinder (130 mm).

What other information is implied or can be looked up?

The steel is, well, steel, so students can look up the specific heat capacity. There are many kinds of steel and we aren’t told what it is, so I suggest that they assume mild steel. Sometimes groups assume different steels. Sometimes they find different values online, which leads to a discussion about sources of information and not always trusting the first Google hit.

The density and latent heat of fusion of ice can be looked up, as well.

The final temperature of the steel will be 0°. We aren’t given the initial temperature, but we can see it glowing yellow-red. That means we can look up what the approximate temperature is. Again we will get a range of values, because the temperature deduced from colour isn’t precise.

Solving the Problem
The fun (and hard work) is over, now it’s time for algebra. This is actually a fairly easy problem. They must:
  • calculate the heat lost when 20 kg of steel cools from red-hot to 0°
  • calculate the mass of ice that could melt
  • calculate the volume of that ice
  • calculate the height of a cylinder with that volume
Different groups will get slightly different answers, because they had different assumptions. This isn’t a problem, as any calculated answer is an approximation anyway.

What Really Happened?
Now that we have predictions, we finish watching the video.

Which assumptions were reasonable? Which turned out to be wrong? Can they refine their numerical model to better reflect what happened?

If your students aren’t used to using a spreadsheet, this is a good time for a mini-lesson on using spreadsheets to test a numerical model with different parameters — for example, changing the geometry of the melted ice, or the initial temperature of the steel.

As an extension, here are two more videos on which they can to test their refined models with. How close can they come to reality?

Remote Learning
This lesson can easily be adapted to remote learning, as long as your students are familiar with breakout rooms. It is harder to monitor what the groups are discussing so small-group discussions may not be as productive.

*My students sit and work in small groups of 3-4 students.
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