Big Ben, Trafalgar Square, Buckingham Palace, and that music TV shows and movies always play when they’re set in England. Yes, today we find ourselves in fair Britannia. And who’s that on the top of the double decker bus? Never mind, thought it was someone I knew.

On this fine day, we find Henri and Cassie not in London, but riding in a dogcart (not actually pulled by dogs) through the English countryside. Our two feline travelers are on their way to a tea party at the country estate where Henri’s dear friend Sir Rupert Bennington of Coventry lives. The name? Oh, he’s a retired show cat. Henri is wearing a blue dress which matches her eyes, while Cassie is wearing a pretty pink party dress.

As you would expect, Cassie is quite excited about visiting an English estate.

“I can’t wait for the jousting,” she cried.

“There’s no jousting,” offered Henri, but Cassie paid no attention.

“Then all the knights will fight a dragon,” the small kitten continued.

“Dragons aren’t …” began Henri, but to no avail.

“Shall I be a damsel in distress or a knight?” wondered Cassie. “I know!” she cried raising a paw into the air. “A damsel in distress who becomes a knight. And my name shall be Lady Cassiopeia of the Round Table.”

The driver of the cart looked back and smiled. “She’s got quite the imagination.”

Henri rolled her eyes. “You don’t know the half of it.”

At last they passed through the gate of Sir Rupert’s estate and made their way up the long drive to the manor house. Awaiting them was a distinguished Persian cat dressed in a short jacket, waistcoat, and ascot. After helping our two feline friends from the cart, he bowed low and kissed Henri’s paw. “Ah my dear Henrietta, it is so wonderful to see you again.”

“Henrietta?” giggled Cassie.

After giving the little kitten a cross look, the older cat turned to their host. “As it is to see you. But please Rupert, you know I much prefer being called Henri.”

“I’d forgotten,” answered Sir Rupert with a hurt look. “Please accept my most sincere apologies.”

Henri smiled. “Of course.” She gestured towards her companion. “Now let me introduce you to my young charge, Cassie.”

Sir Rupert bowed and kissed Cassie’s paw. “Enchanted to meet you young kitten.”

Cassie blushed and held her paw close to her. However, the spell only held for a moment as she blurted out, “where are all the knights?”

Henri looked over at the kitten with embarrassment. “I’m sorry. I told her before there were no knights, but she wouldn’t listen.”

Sir Rupert broke into a wide grin. “Ah, but there are! And if you follow me I’ll be glad to show you.”

Sir Rupert led them into the house and upstairs to a long hallway which contained suits of armor lined up on either side of it. “This,” explained Sir Rupert gesturing around them, “is where the knights store their armor when not off in battle or saving fair damsels.”

Cassie ran down the hall looking at each one. “Wow,” she cried. “Where are all the knights now?”

Sir Rupert gave Henri a wink. “Alas, they’re all off getting their knighting licenses renewed. Every year they have to take a special test to make sure they’re still worthy of being knights.”

“Aww,” muttered the disappointed kitten. “I really wanted to meet a knight.”

“But you have young Cassie,” offered Sir Rupert with a bow while giving Henri a knowing smile. “For I was once a knight myself. How do you think I became Sir Rupert?”

Cassie ran over to him. “Really?” she cried. “Can you tell me about some of your adventures?”

“I’d be most happy to my young kitten,” answered Sir Rupert, “but first we have a tea party to attend. After that I’ll tell you stories that will make your fur stand on end.”

“Hooray!” shouted an excited Cassie.

The three of them went downstairs and out to the garden where a large tent had been set up for the tea party. Near the center of the tent was a large table upon which sat a large fish sculpted out of ice.

Seeing it, Cassie started jumping up and down. “We get fish! We get fish!” she squealed.

“Calm down,” scolded Henri several times before she was able to get Cassie’s attention. “That’s not a real fish, it’s carved out of ice.”

“Oh,” answered Cassie, not entirely convinced. She decided she’d get a closer look later when Henri wasn’t paying attention.

As other guests were now starting to arrive, the three cats found an out of the way table to sit at to avoid getting their tails stepped on. Henri poured some tea into a cup for Cassie and put some cookies on her plate. “Do you want cream in your tea?” she asked.

“Not right now,” answered Cassie. “I’ll put the cream in right before I drink it so the tea stays nice and hot.”

“It doesn’t work that …” began Henri, but Cassie interrupted her.

“Can I go outside and look at the garden?”

“Okay, but be sure you don’t get your dress dirty.”

“I won’t. Thanks,” answered Cassie before running off.

With the young kitten gone, the two older cats began to reminisce about old times and what they’d been doing since they’d last seen one another. It wasn’t long before the kitten returned.

“The garden’s boring,” she moaned, putting cream into her tea and taking a sip.

“It’s cold,” she complained.

“Mine is still nice and warm,” noted Henri taking a taste. “Wonder why that is?”

The two older cats glanced at each other with mischievous grins and each raising a paw upward cried out together, “it’s physics!”

“Oh great,” grumbled Cassie. “Now I’m getting it in stereo.”

Leaving the two laughing cats behind, Cassie decided this would be the perfect time to check out the fish. Walking around the table, she studied it carefully. It sure looked like a fish, but it didn’t smell like a fish. Must be because it’s frozen, she thought.

Then she noticed that on some of the other tables were cups with the remnants of ice cubes in them. Most of the ice cubes were almost entirely melted, but the fish looked exactly the same. She looked back over at Henri and Sir Rupert and thought, if the fish were made of ice it would have melted like the ice cubes. Henri must have told me that it was made of ice so I wouldn’t try and eat it. Well, I’ll show her.

Cassie jumped up on the table, approached the fish, and gave it a lick. Unfortunately, once her tongue touched the fish, it wouldn’t let go. She tried to pull back, but it did no good and hurt a lot.

A muffled “halp!” was all she was able to get out.

Noticing the commotion, Henri rushed over with Sir Rupert close behind. “Cassie!” she cried. “Don’t move, we’ll get you free.”

Climbing up beside the trapped kitten, Henri took a glass of water from Sir Rupert and carefully poured it where the kitten’s tongue was stuck to the fish. In a minute she was free, and Henri helped her back to the table. A cup of warm tea was just the thing to make Cassie’s sore tongue feel better.

The little kitten looked down and hid her head under her paw. “I thought the fish was real. All the ice cubes melted, but the fish didn’t. I just thought you didn’t want me eating the fish. I’m so sorry.” Tears filled her eyes.

Henri patted Cassie paw. “Please don’t cry. No damage was done and, more importantly, you weren’t hurt. That’s what matters.”

The little kitten sniffled. “But why didn’t the fish melt like the ice cubes?”

“What do you think?”

In a small voice Cassie answered. “Physics?”

“Yes, physics,” answered Henri with a smile, giving Sir Rupert a wink.

“Now young kitten,” began Sir Rupert, “I promised to tell you about some of my adventures as a knight. Let’s adjourn to the sitting room so I can tell you about the time I had to save a kingdom from a dragon.”

“A real dragon? Wow!” cried Cassie suddenly feeling much better as the three of them headed inside.

Poor Cassie. Well maybe in the future she’ll listen to Henri. No, I don’t think so either. At least Cassie’s opinion of physics seems to have improved. And speaking of physics, Henri and Sir Rupert clearly saw some in our story, so let’s see if we can find it too.

Hot tea, melting ice, the warmth of the sun on your face, and the furnace keeping your house toasty in the winter. What do all these thing have in common? If you guessed heat, you’d be right. And what exactly is heat? It’s a form of energy, and like all energy, heat energy (or thermal energy) is conserved as specified in the First Law of Thermodynamics which in its simplest form can be expressed as:

The total energy of a closed system is constant.

Now wait a minute. Tea gets cold, so how can we possibly say heat energy is conserved? Notice that the First Law of Thermodynamics refers to a “closed system”. A closed system is defined as a volume that energy cannot enter or escape from.

For example, if we put the cup of hot tea in an insulated air tight box and wait, the tea and air will eventually reach a temperature slightly higher than the original air temperature. The total thermal energy in the box hasn’t changed, but the heat from the tea has dissipated into the surrounding air.

I know what you’re thinking. If the amount of thermal energy is the same, why did the temperature go down? That’s because temperature isn’t a direct measure of energy. Thermal energy is only part of what determines how hot something gets. Let’s say you put two pots of water on the stove with the burners set to high. One’s a small sauce pan and the other’s a giant pot. Which one will boil first? The smaller one, of course.

That’s because how hot something gets is also a function of its mass. Therefore, it takes more energy to get the larger pot of water to come to a boil. This is the concept of thermal mass, which we’ll discuss in more detail shortly.

Now back to our tea sitting in the box. This example illustrates another interesting principle of thermal energy: it doesn’t like to be different. An object which is hotter than the surrounding area will dissipate its thermal energy until it reaches the same temperature as the area around it. This process is known as conduction.

Okay, so far we’ve seen that thermal energy is conserved and is a conformist. How exactly does a hotter object shed its excess energy to the surrounding area? To understand that, we need to take a look at what’s happening at the molecular level. Molecules are always in motion and how quickly they move is determined by their temperature. Maybe you’ve heard the term “Absolute Zero?” That’s the temperature at which molecules lose all their energy and stop moving.

To understand this, think about what would happen if you put an ice cube in a pan on a hot stove. The ice cube eventually melts into water, which in turn becomes steam. As the water molecules move faster, they can no longer remain in solid form and then as they move faster still, the water turns into a vapor.

So in the hot tea we have molecules flying around and some of them will collide with the slower moving molecules from the side of the cup. So how exactly does this cause the tea to cool? Any object in motion has kinetic energy and the faster it’s moving the more kinetic energy it has. Thus, the molecules in the hot tea have more kinetic energy that the molecules in the cup. Let’s look what happens when Mr. Tea Molecule and Mr. Cup Molecule run in to each other.

When are two molecules run into each other, this is called an elastic collision. The total kinetic energy of the two molecules remains the same, but some of Mr. Tea Molecule’s kinetic energy is taken by Mr. Cup Molecule. Thus, Mr. Tea Molecule slows down (and gets cooler) while Mr. Cup Molecule, now with more kinetic energy, speeds up (and gets warmer). This happens every time the tea and cup molecules collide until they have the same kinetic energy (kinetic energy equality for all!) and thus the same temperature.

Considering the complexity of the process, the equation defining the conductive heat transfer between two objects is surprisingly simple.

The minus sign in the above equation is because conductive heat transfer causes an energy loss in the hotter object.

Okay, so we can calculate the thermal energy leaving the tea, but I’d really like to know how its temperature changes. How do we do that? Every material has a property called specific heat (C) which is defined as the amount of energy required to increase the temperature of one gram of the material by one degree Celsius. Notice that the specific heat is a function of the mass of the material. This goes back to the concept of thermal mass we mentioned previously. The more mass an object has, the more energy it takes to increase its temperature. Now that we have everything we need, the temperature change of the tea every second would be:

Okay now why was Cassie’s tea cooler than Henri’s? The only difference was that Henri put her cream in right away while Cassie didn’t put her cream in until right before drinking the tea. Let’s use the above equation to figure this out. The plot below compares the temperature of Henri’s tea with the temperature of Cassie’s tea after she finally added the cream.

Wow! Adding the cream right away sure makes a big difference. Only waiting four minutes (240 seconds) to add the cream results in Cassie’s tea being 10 degrees cooler than Henri’s. But why?

The heat flux equation is a function of the temperature difference of the two objects. When Henri added her cream, the temperature difference between her tea and the air around it went down. However, by not adding cream, Cassie’s tea had a larger temperature difference with the air so its heat flux (energy loss) was greater. Thus, when Cassie finally added the cream, she ended up with a colder cup of tea.

So let this be a lesson to you: if you want your tea (or coffee) to stay hot longer, put the cream in right away. Most people have to go to Starbucks University to learn that.

However, there’s one last mystery we need to solve. Why didn’t the ice fish melt as quickly as the ice cubes? I’m sure you already know the answer. That’s right, it’s because it has much more mass than the ice cubes, so it takes a lot more energy (and time) for it to melt.

Cassie would’ve saved herself a lot of trouble if she’d known this. She’ll learn in time, and in the end I think everything turned out all right. Well, unless Sir Rupert has some swords hanging around, then we might have reason to worry. However, we’ll leave that concern for another time.