Newton's law of cooling facts for kids

Newton's law of cooling is a simple rule in physics that helps us understand how things cool down. It says that a hot object loses heat faster when there's a bigger difference between its temperature and the temperature of its surroundings.

Think of it like this: A super hot pizza cools down very quickly when you first take it out of the oven. But once it's only a little warmer than the room, it cools much slower. This is because the "rate of heat loss" (how fast it cools) is directly connected to how much hotter the object is compared to its environment.

This law works best when the temperature difference isn't huge, and when the way heat moves (like through air or water) stays the same. It's often used to describe how objects cool down through thermal conduction (heat moving through a material) or convection (heat moving with a fluid like air or water).

When you put this law into a math equation, it shows that an object's temperature difference from its surroundings usually drops in an exponential way over time. This means it cools quickly at first, then slower and slower.

The History Behind Newton's Law

Isaac Newton, a famous scientist, first wrote about this idea in 1701. He published his work without his name on it in a science journal called Philosophical Transactions.

Newton didn't originally write the law exactly as we use it today. He noticed that the speed at which an object's temperature changed was related to the temperature difference between the object and its surroundings. Back then, people sometimes confused "heat" and "temperature," which are related but different ideas. Scientists later clarified these concepts.

In 2020, some scientists named Maruyama and Moriya redid Newton's original experiments using modern equipment. They found that Newton's measurements from the late 1600s were actually "quite accurate" for his time, even considering things like thermal radiation (heat from light) and how air moves around hot objects.

How Cooling Works with Newton's Law

Newton's law of cooling is often used to explain how things cool down through convection, which is when heat moves through a fluid like air or water.

The law works very well for things like a fan blowing air over a hot object (called "forced convection"). In these cases, the "heat transfer coefficient" (a number that describes how easily heat moves) stays pretty much the same.

However, for "natural convection" (like a hot object cooling in still air, where warmer air naturally rises), the law is only an approximation. This is because the speed of the air movement changes with the temperature difference, making the heat transfer a bit more complex. Newton himself knew about this limitation.

For very large temperature differences, or when heat is mainly transferred by radiation (like the heat you feel from a hot stove without touching it), Newton's law isn't as accurate. Radiative cooling is better explained by another law called the Stefan–Boltzmann law, which says that heat transfer depends on the fourth power of the absolute temperatures.

Understanding the Math (Simply)

While the full math can look complicated, the main idea of Newton's law is simple:

The rate at which an object loses heat depends on:

• How big the temperature difference is between the object and its surroundings.
• How much surface area the object has (a bigger surface means more heat can escape).
• A "heat transfer coefficient," which is a number that tells us how easily heat moves between the object and its environment. This number depends on the materials involved and how the heat is moving (e.g., through air or water).

Imagine you have a hot object. The equation basically says: How fast heat leaves = (heat transfer number) x (surface area) x (object temperature - environment temperature)

This means if the object is much hotter than its surroundings, or if it has a large surface area, it will lose heat very quickly.

When Newton's Law Works Best

There's a special number called the Biot number that helps scientists decide if Newton's law of cooling will be very accurate for a situation.

Imagine a hot metal ball cooling in water. Heat has to move from the center of the ball to its surface, and then from the surface into the water. The Biot number compares how hard it is for heat to move inside the object versus how hard it is for heat to move from the surface to the outside.

• If the Biot number is very small (less than 0.1), it means heat moves very easily inside the object. So, the whole object pretty much stays at the same temperature throughout, even as it cools. In this case, Newton's law works really well, and the object's temperature will drop smoothly over time.
• If the Biot number is large, it means heat doesn't move easily inside the object. So, one part of the object might be much hotter than another part, even while it's cooling. In these cases, Newton's law isn't enough, and you need more complex equations to understand how the temperature changes in different parts of the object.

So, for simple cooling problems where the object's temperature is pretty uniform inside, Newton's law is a great tool!

See also

• Thermal transmittance
• List of thermal conductivities
• Convection diffusion equation
• R-value (insulation)
• Heat pipe
• Fick's law of diffusion
• Relativistic heat conduction
• Churchill–Bernstein equation
• Fourier number
• Biot number
• False diffusion
• Mpemba effect