# Heat Transfer Through Conduction: Equation & Examples

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• 0:05 What is Conduction?
• 1:45 Examples of Conduction
• 3:13 Calculation Example
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Lesson Transcript
Instructor: David Wood

David has taught Honors Physics, AP Physics, IB Physics and general science courses. He has a Masters in Education, and a Bachelors in Physics.

After watching this lesson, you should be able to explain how heat transfers by conduction, give examples of conduction and complete conduction calculations. A short quiz will follow.

## What Is Conduction?

When I was a kid, I hated getting up in the night to use the bathroom. Not only did it make it hard to get back to sleep, but the bathroom floor was tiled and super cold. I would run across the tile to the rug, feeling like my feet were burning.

Perhaps you've noticed how your feet feel when you step from a carpeted room into a tiled room. Which floor surface is colder?

The floor of a tiled room pretty much always feels colder. But they're actually exactly the same temperature. Whenever you're in a room that has been sealed off for a while, with no windows and doors open, it won't take long for everything in the room to reach thermal equilibrium, or equal temperature.

So why do tile floors feel colder? It's all because of thermal conductivity.

Conduction is the passing of heat energy between two objects that are in direct, physical contact. It is one of the three types of heat transfer, the other two being convection and radiation. Whenever two objects of different temperatures are in contact with each other, heat energy will pass between them.

To understand this, we have to realize that temperature is the average kinetic energy of the molecules in a substance. Hotter materials have molecules that are moving faster. So when a cold object and a hot object are touching, the fast moving hot molecules will hit the colder molecules, spreading the heat from the hot object into the cold object. This will keep happening until they reach the same temperature.

But that says nothing about how fast it will happen. Some materials are better conductors than others. Your feet are pretty much always warmer than the floor, but a tile floor conducts heat faster. What your skin feels as 'cold' is just the heat transferring from your feet into the floor, and it happens much faster with a tile floor than with a carpet.

## Examples of Conduction

There are all kinds of examples of conduction in our everyday lives. The key is to think about whether objects are physically touching. So a saucepan of boiling water being heated by an electric stove is receiving heat energy from the stove by conduction. And when you touch a metal cookie sheet in the oven and burn yourself, that also happened due to conduction.

## Conduction Equation

In physics, everything must have an equation! It's kind of an unwritten rule. Conduction is no exception. How fast conduction happens depends on several factors: what material the objects are made from (the conductivity), the surface area of the two objects in contact, the difference in temperature between the two objects, and the thicknesses of the two objects.

In equation form, it looks like this.

Q over t is the rate of heat transfer - the amount of heat transferred per second, measured in Joules per second, or Watts. k is the thermal conductivity of the material - for example, copper has a thermal conductivity of 390, but wool has a thermal conductivity of just 0.04. T1 is the temperature of one object, and T2 is the temperature of the other. Since it's a temperature difference, you can actually use Celsius or Kelvin, whichever is most convenient. And d is the thickness of the material we're interested in.

So the rate of heat transfer to an object is equal to the thermal conductivity of the material the object is made from, multiplied by the surface area in contact, multiplied by the difference in temperature between the two objects, divided by the thickness of the material.

## Calculation Example

Okay, let's go through an example. Let's say you're going to a water park, and you're going to take a Styrofoam cooler with you. The cooler has a total surface area of 1.2 meters squared, and the walls are 0.03 meters thick. The temperature inside the cooler is 0 Celsius, and at the hottest part of the day it's 38 degrees Celsius. During this time of day, how much heat energy per second is lost by the cooler? And how much heat energy is lost in three hours at the water park assuming the temperature stays at 38 degrees? (Note: The thermal conductivity of Styrofoam is 0.01.)

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