Does Temperature Change Smoothly When Water Is Heated?

FROM THE LECTURE SERIES: UNDERSTANDING THE MISCONCEPTIONS OF SCIENCE

By Don Lincoln, Ph.D., Fermi National Accelerator Laboratory (Fermilab)

There are a lot of misconceptions of how heating things work that are less subtle than the ones revolving around entropy. How do you react to the idea that putting a pan of water over a fire will constantly heat it up with a smoothly changing temperature? Does that sound reasonable to you? Let’s find out.

Image of a pan on an electric stove with water boiling in it, and faint traces of steam rising up.
It takes 2030 units of energy to boil water, which is more than double the amount of energy it takes to melt ice and bring it up to the boiling temperature. (Image: New Africa/Shutterstock)

Temperature Change Is Never Linear

Suppose you took a kilogram of ice and put it in a very strong and sealed metal container and started heating up the container. To monitor what’s going on, you put a thermometer into the ice before you froze it. To make the experiment easy to interpret, you put the same amount of energy into the container every minute. In other words, you put the container over a nicely constant flame.

Let’s imagine that you took the ice out of a typical home freezer, which is set at –20° centigrade, or just shy of 0° Fahrenheit. And then you heated it up to 120° centigrade, or just about 250° Fahrenheit.

Most people would think that the temperature of the ice, then water, then steam, would change constantly as the energy was constantly added. The following graph shows what most people would commonly think.

Image shows a graph with temperature on the y-axis and units of energy on the x-axis, with a straight diagonal line in the center, starting from the bottom left corner toward the top right corner.
It’s a common misconception that there’s a constant change in temperature of water as energy is added. (Image: TGCD)

It turns out that it takes just shy of 2900 units of energy to heat ice from –20° centigrade to 120° centigrade. And, if you focus on the shape, it is just a straight line—a constant change in temperature as energy is added. However, that is not what actually happens when you really do the experiment.

If you slowly and constantly added about 2900 units of energy, you’d see the temperature go up, and then stay constant at 0° centigrade, and then go up again, then stay constant at 100° centigrade, and then go up again.

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Boiling Water Requires Double the Energy Input Than Melting Ice

0° and 100° centigrade, which are 32° and 212° Fahrenheit, are the freezing and boiling temperatures of water.

The following graph shows that you can heat the ice by adding energy. But then the temperature stays at the melting point of ice for a long time without changing. It takes 42 units of energy to heat the ice from –20° to 0° centigrade. Then it takes 334 units of energy to melt the ice.

Once the ice has turned into water, you can then warm up the water pretty easily. It takes 420 units of energy to bring the temperature from 0° centigrade to 100° centigrade. That’s more energy than it takes to melt the ice into water.

Image of a graph with temperature on the y-axis and heat energy on the x-axis, and a line that starts in the bottom left corner, rises up to zero degree centigrade and flattens, then rises up to 100 degree centigrade and flattens, and finally rises to   120 degree centigrade and ends.
If you slowly and constantly add energy, the temperature goes up, then stays constant for a while, then goes up again, then stays constant again, and then goes up again. (Image: TGCD)

The really interesting thing is when water gets to 100° centigrade. You can see in the graph that it stays at that temperature for a long time. You have to put a lot of energy to boil the water and turn it into steam. In fact, it takes 2030 units of energy to boil water. That’s more than double the amount of energy it takes to melt the ice and bring it up to the boiling temperature.

Then, when all the water is boiled away and turned into steam, it becomes easy to raise the temperature of the steam. It only takes 40 units of energy to raise the temperature by a further 20° centigrade.

So, while it doesn’t take much energy to change the temperature of ice or steam, it takes about twice as much energy to change the temperature of water 1° compared to ice and steam.

However, the big energy hogs are the melting and boiling stages, and especially the boiling one. It’s the phase transitions that really eat up energy.

This is a transcript from the video series Understanding the Misconceptions of Science. Watch it now, on The Great Courses Plus.

Changing the Temperature of Water Requires a Lot of Energy

Another thing that doesn’t count as a misconception per se, but is perhaps a little known fact, is that it’s very difficult to change the temperature of water. You can compare it to most common metals, like steel, for example.

If you took a certain amount of energy that would increase the temperature of a kilogram of water by 1° centigrade, that same energy would raise the temperature of the metal by 8° centigrade. And it’s not just a metal thing. It’s twice as hard to heat up water as it is to heat up alcohol. Another surprising thing is that it is five times easier to heat up asphalt than water.

When you get right down to it, water is basically an enormous heat sponge. It can soak up a huge amount of energy without changing its temperature much. And the opposite is true as well. When water does change its temperature, it does so by absorbing a lot of energy and becomes much harder to cool off.

This is the reason why if you live near a coast, the temperatures on the shoreline are much more temperate than just 50 miles inland. The same Sun is beating down on the dirt and the water, but the temperature of the dirt changes by 5° for every degree that the water does.

And in the winter, the ground gets cold and freezes much faster than a lake does. So the coastal winters are generally milder, at least temperature-wise, than inland.

Challenges in Thermodynamics

The study of thermodynamics has more misconceptions than most branches of physics. Everyone is generally familiar with how things heat and cool, but it’s not like that they can see the energy move around. It’s different with the physics of projectiles and cars and balls getting dropped. We can see those things happen, which allows us to build better intuitions about them.

However, that is not the case with heat and heat energy. For those, we need to use indirect instruments. We need accurate thermometers and devices for measuring energy. It’s the reason that while we knew a lot about the physics of motion in the 1500s and 1600s, it wasn’t until the 1800s, and even into the 20th century, that thermodynamics started to yield its secrets.

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Common Questions about Heating Water and Temperature Change

Q: How much energy is required to boil water?

It takes 2030 units of heat energy to boil water, which is more than double the amount of energy required to melt ice and bring it up to the boiling temperature. So, if sufficient energy input is not available, water will not boil.

Q: Why does it take more energy to raise the temperature of water?

Water is like an enormous heat sponge. It can soak up a huge amount of energy without changing its temperature very much. This is the reason why after reaching 100° centigrade, water stays at that temperature for a long time, and a lot of energy is required to boil the water and turn it into steam.

Q: How do large bodies of water affect temperature?

Since water acts as a heat sponge, if you live near a coast or a large water body, the temperatures on the shoreline are much more temperate than 50 miles inland. The Sun heats up the ground quicker than water, and the temperature of the ground changes by 5° for every degree that the water does. On the other hand, during winter, the ground gets cold and freezes much faster than a water body does. So the coastal winters are generally milder than inland.

Q: Does water heat up slowly or quickly?

It’s very difficult to change the temperature of water. For example, if you took a certain amount of energy that would increase the temperature of a kilogram of water by 1° centigrade, that same energy would raise the temperature of the metal by 8° centigrade.

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