Case Study 1 — Pat Hammond and the Borrowed Kettle

It is the second Tuesday of October, in a small Ohio town called Maddenburg, and Pat Hammond is in front of a third-period AP Chemistry class with a borrowed electric kettle, a graduated cylinder, a candy thermometer, and thirty teenagers who are not, at this particular moment in the school year, especially impressed with chemistry.

Pat has been teaching for twenty-eight years. She knows the look. It is the eight-week-into-the-semester look — past the polite attentiveness of the first weeks, before the sudden alertness of midterm-week panic. The students are tired. They have been doing molarity calculations for three days in a row. They have arrived at the conclusion, unspoken but visible, that chemistry is largely about plugging numbers into equations and getting different numbers out.

Pat is going to fix this in the next forty-three minutes, with water.

She has done this demonstration before. She has done it almost every fall for fifteen years, and it works almost every time. She borrowed the kettle from the principal's office because her own classroom kettle finally died over the summer.

"Today's a hands-off demo day," Pat says. "Phones in the basket. I want eyes on the kettle."

Phones go into the basket. There are some sighs. The basket is at the back of the classroom; she invented the basket five years ago and it has been one of her most successful interventions.

She holds up the empty kettle.

"Let's start with what we know. This is water. I'm going to put it in this kettle. The kettle plugs in over there. The kettle has a heating element. The heating element is going to do work on the water — transfer energy to it. Stiles, what's the energy unit?"

A boy in the back: "Joules."

"Joules. What happens to the temperature of the water as I add joules?"

A girl, two rows up: "It goes up?"

"It goes up. Predict for me — and I want you to actually commit to this — what is the relationship between joules added and temperature increase? Linear? Exponential? Logarithmic? Show me with your hand."

Most of the class makes a flat upward-sloping line with a finger. A few make a curve.

"Most of you said linear. We'll see. Marisol — set up the candy thermometer in the cylinder so we can read it from the chairs. Yes, like that."

She fills the kettle with cold water from the tap. She measures 500 mL into a beaker first, then pours it into the kettle. She wants the volume known.

"So we have 500 grams of water — water has density of 1 g/mL — at the temperature of the tap. Marisol, what's the thermometer reading?"

"Seventy-eight."

"Fahrenheit?"

"Yeah."

"What's that in Celsius?"

A pause. A boy named Tariq, who is good at quick math: "Twenty-five. Or close. Twenty-five point five."

"Close enough. Twenty-five point five Celsius. Initial temperature." She writes T₀ = 25.5°C on the whiteboard, which she has divided into a temperature column and a time column. "What's our specific heat capacity for water, somebody? It's in the back of your book."

Several voices: "4.18 joules per gram per degree."

"4.18 J per g per °C. So to raise our 500 g of water by 1°C — how many joules?"

"4.18 times 500. Two thousand ninety joules."

"2,090. To raise from twenty-five point five to one hundred — that's about seventy-five degrees of climb. Multiply through. How many joules total?"

The class is doing math now, calculators or fingers. Tariq beats everyone again: "About a hundred fifty-seven thousand joules."

"157,000 J. Hold that number." She plugs in the kettle. "This kettle is rated 1,500 watts. A watt is a joule per second. So in one second, it puts in 1,500 J. To put in 157,000 J at 1,500 J per second takes about 105 seconds. Predict how long until the water reaches 100°C."

"Hundred and five seconds?"

"At absolute peak efficiency, no losses. In reality, more like two minutes. Marisol, you've got the stopwatch?"

"Got it."

"Mark me a time when it hits 30, 50, 70, 90, 95, 99, and 100. And don't take your eyes off it once we get past 95."

The kettle starts. The class watches. Pat doesn't say anything for almost a minute. The kettle hisses softly.

"Thirty," Marisol calls out at thirty-three seconds. "Fifty at sixty-eight."

"What's the rate so far? About a degree per second?"

"Yeah."

"That track linear?"

"It's tracking like a degree per second, yeah."

"Okay. Stiles, what does that mean for our prediction of when it hits 100?"

Stiles, in the back, doing math: "One-oh-seven, one-oh-eight seconds."

"Hold the prediction."

"Seventy at ninety," Marisol says. "Ninety at one-twenty."

The class is genuinely watching now. Some of them are leaning forward. The thermometer is climbing.

"Ninety-five at one-thirty-three. Slowing down."

"Slowing down?"

"It's not a degree a second anymore. Ninety-six at one-thirty-eight. Ninety-seven at one-forty-three."

"What's the rate now?"

"Less than half. Like point three a second, maybe."

"Why is it slowing? Is the kettle giving less power?" Pat asks. The kettle is still humming. The element is glowing under the water.

"Maybe it's like — the water at the top is cooler, so it has to get to all of it?"

"That's part of it. Convection. The currents take time to mix the heat up to the surface where the thermometer is. But there's something else. Watch what happens at the bottom."

The class can see, through the side of the kettle, small bubbles starting to form on the heating element. They are sticking, growing slightly, then dislodging and rising.

"Bubbles at the bottom," someone says.

"What's in the bubbles?"

"Air?"

"Some air. It's mostly water vapor. Steam. The water at the bottom is hottest — closest to the element — and some of it's already turning to gas. What temperature does water boil at?"

"100°C."

"At sea level. So the water at the bottom is at 100°C, but the bulk of the water is still at 97 or 98. The bubbles rise and condense back into liquid as they hit cooler water above them — they're not making it to the surface yet. But as the bulk gets hotter, the bubbles start surviving."

"Ninety-eight at one-fifty," Marisol says.

"Predict to me. When does it hit 100?"

The class is divided. Some say ten more seconds, some say thirty, some say a minute.

"Ninety-nine at one-fifty-eight. Ninety-nine point five at one-sixty-five."

"How long are we from boiling now?"

"It's at the surface — there are bubbles all the way to the top now. Rolling. It's at — ninety-nine point eight at one-seventy."

"And now?"

"One hundred. One hundred. One hundred."

The class waits. The thermometer holds at 100°C. The kettle is roaring with steam now, water visibly evaporating from the spout.

"What temperature is it now, Marisol? It's been at boiling for thirty seconds."

"Still one hundred."

"After a minute?"

"Still one hundred."

A boy in the third row, Marcus — the same Marcus, by the way, who Pat had told the author about, the one who became a welder — raises his hand.

"Mrs. Hammond, the kettle is still putting in 1,500 watts. Where is the energy going?"

Pat smiles. This is the moment. This is why she does the demo every year.

"That, Marcus, is the question. What you're seeing is a phase change. The water is converting from liquid to gas. To do that, the molecules have to be pulled apart from each other — they have to break the bonds holding the liquid together. Those bonds are hydrogen bonds, and breaking them takes a lot of energy. The energy from the kettle is going into breaking those bonds. Not into raising the temperature. The temperature can't go higher than 100°C while there's still liquid water in the pot, because every bit of additional energy goes into vaporizing more water, not heating what's left."

"How much energy does it take to vaporize?" Marcus asks.

"About 2,260 joules per gram. To vaporize 500 g of water entirely — to boil this kettle dry — you'd need about 1.13 million joules. At 1,500 watts, that's twelve and a half minutes of full-power kettle time. Five times the energy it took to heat the water from cold to boiling in the first place."

"Five times?" several voices say.

"Five times. The phase change is much more energy-intensive than the heating. This is called latent heat of vaporization. Latent because it doesn't show up on the thermometer — the temperature doesn't change while the energy is being absorbed. The energy is hidden in the steam."

A girl in the front row, Imani, asks the question Pat has been waiting twenty-eight years for some student to ask: "Mrs. Hammond, is that why steam burns are so bad?"

Pat almost laughs out loud with delight.

"Imani, yes. Steam burns are worse than boiling-water burns because the steam carries that 2,260 joules per gram with it. When steam touches your skin, it condenses — turns back into liquid water — and dumps all of that latent heat into your skin in an instant. Boiling water at 100°C and steam at 100°C are at the same temperature, but the steam is carrying five times the energy."

She turns the kettle off. The steaming dies down within a minute. The class is quiet.

"This is why your grandmother told you not to lift a pot lid toward your face. This is why you should always tip a kettle's spout away from your hand. This is also why steam is one of the most efficient ways to cook — the same physics that makes steam dangerous to your skin makes it spectacularly good at cooking dumplings, fish, and eggs. The steam condenses on the cool food and dumps its latent heat into the food. The food cooks fast and gentle."

She picks up the chalk. On the board, next to where she had written the temperature curve they had measured, she draws a horizontal line at 100°C and labels it with an arrow pointing up: all energy goes into phase change. She labels the climbing portion: energy raises temperature. She labels the boundary between them: latent heat.

"In tomorrow's class we're going to do the math on this — how much energy to boil away X grams of water, how much energy to melt ice, how to use this in cooling systems. But for tonight, I want you to think about every kettle in your house and every pot on every stove in your life. Every one of them, when it's boiling, is at 100°C and stuck there until the water is gone. The energy doesn't disappear. It's hiding in the steam. The kitchen has been this way your entire life. You just didn't know."

The bell rings. The class, slowly, gathers their things. Imani lingers at the front desk.

"Mrs. Hammond, can we use this for the lab next week?"

"What did you have in mind?"

"Like — measure how long it takes for different amounts of water to boil? Or with a lid versus without?"

"That's an experiment, Imani. Sketch it out. Bring it Friday and we'll see if it'll fit."

Imani goes. The classroom empties. Pat unplugs the kettle. She refills it from the tap and sets it on the back counter, ready for tomorrow's freshman general chemistry class, where she will do the same demonstration again with a different group of teenagers and the same water, and the bond network in the same H₂O will be the unsung star of yet another forty-three-minute period.

She picks up her chalk and erases the board. Tomorrow she will fill it again.

Analyze this: Pat structures the demonstration to elicit predictions from the students before showing them the result. Why is this pedagogically important? What changes in a student's understanding of latent heat when they have predicted something else and then watched their prediction fail?

The kettle in the demonstration is rated at 1,500 watts. Pat calculated that, at perfect efficiency, it would take about 105 seconds to bring 500 g of water from 25.5°C to 100°C — but the actual time was around 175 seconds. Where did the missing time go? List three sources of energy loss in a real kettle. (Hint: think about the kettle's body, the surrounding air, and the lid.)

Marcus's question — "where is the energy going?" — is the pivotal moment. If you were teaching this demonstration, what alternative questions could you use to elicit the same insight if no student spontaneously asked? Draft three.

The chapter argues that the kettle demonstration is one of the most important experiences a chemistry student can have. Do you agree? Is there a better demonstration of latent heat for a high-school chemistry class? Justify your answer.