Hello there! Welcome to lecture 16: heat transfer!
Heat transfer describes how heat moves from one place to another. It is useful to understand everything from how a stove works to cook food to how our climate works. Understanding how heat moves around also enables us to create technology that can keep things hot or cold.
Each of the following concepts will be discussed in this video: conduction, convection, electromagnetic radiation, the greenhouse effect, engineering heat transfer, solar power, and Newton’s law of cooling.
There are three types of ways that heat can move from one place to another: conduction, convection, and electromagnetic radiation.
Conduction is heat transfer that occurs due to physical contact between objects. Conduction also explains how heat is able to transfer within an object.
Temperature relates to the average energy of molecules. If molecules are able to easily bump into each other, causing collisions that transfer energy from one place to the next, then those types of substances will be good heat conductors. Good heat conductors tend to be solids, where molecules are in close physical proximity. In liquids and gases, where molecules are spread farther apart, it’s harder for heat to conduct due to these atomic collisions.
In fact, the solid objects that make the best heat conductors tend to be those that also make the best electrical conductors: metals. In metals, electrons are capable of moving around readily, which causes very efficient transfer of heat energy from one part of a metal to another.
Let’s look at an example of this. In this video, I’ve placed two pretty much identical ice cubes onto different black plates. One of the plates is metal, and the other one is plastic. Metal is a good heat conductor. Plastic is not a good heat conductor. What happens is that the metal is able to conduct heat from the surrounding air into the metal plate and thus into the ice cube very efficiently. That ice cube melts very rapidly.
On the other hand, the plastic plate is a bad heat conductor, or a good heat insulator. That means that it keeps the heat in the atmosphere away from the ice cube, and that ice cube barely melts at all. Note that both ice cubes are surrounded on five sides by air. Air, being a gas, is a very bad heat conductor. When the ice cube on the metal plate melts, it melts predominantly from the bottom, the side that is in contact with the good heat conductor.
This demo also explains why metal objects tend to feel cold to the touch. When you touch something metal, that metal is able to conduct the heat from your hand away very readily. Similarly, objects made of bad heat conductors, things like plastic, wood, paper, cork, and other insulators, are not going to feel cold to the touch, unless they themselves are cold.
Even among metals, different metals have different amounts of heat conductivity. In this video, I have an apparatus with four different metals that connect to a central plate. I’ve placed candles into each of the metals, and then lit a Bunsen burner under the central plate. As that central plate heats up, it conducts heat to each of the four metals. The metal that heats up the fastest, that has the highest heat conduction, will melt the candles quickest.
First, you can see that the heat is going to travel outward. That is to say, the candles closest to the central plate melt first. Second, you can see that the best heat conductor melts the candles the fastest.
That best heat conductor is copper, which contains all of the green candles. The next best heat conductor is aluminum, which contains all of the yellow candles. Then comes brass, with the blue candles. Finally, the worst of the heat conductors of these four metals is iron, which has the red candles.
Remember, heat conduction requires physical contact between materials, or within a material. When you put food onto a frying pan to cook it, that food will cook due to that physical contact: heat conduction. This is why frying pans are made out of metals, good heat conductors! The part of the frying pan we have to touch is frequently covered with plastic or is very long and far away from the center of the frying pan, keeping our hands safe from the heat of the stove.
One last thing about heat conduction: Don’t confuse heat conduction with specific heat capacity! While they seem similar, they are actually two completely different things. Heat conduction quantifies the ability of a material to move heat from one place to another. Specific heat capacity quantifies how much heat is required to change the temperature of a certain amount of material.
The next type of heat transfer is known as convection. Convection is heat transfer that comes about due to the motion of molecules themselves. The types of materials that are good at convection are the types of materials where molecules can move around very freely – liquids and gases.
If you’ve ever held your hands above a toaster while heating something up, you’ve experienced convection. Air in close proximity to the toaster coils heats up. As that air heats up, it becomes less dense than the surrounding air, causing it to rise. When you hold your hand above the toaster, you are experiencing that warm air rising up.
In this demo, I have a large beaker filled with water that’s a little bit colder than room temperature. I place inside of that beaker a smaller flask filled with hot dyed water. The dye is just there to help us visualize the motion of the molecules in that flask. What happens is that the hot water, being less dense than the surrounding cool water, is going to experience a buoyant force that causes it to rise up. You can see this from the dyed water moving upward in the beaker.
Eventually, as the hot water moves upward, it exchanges heat energy with the cool water, causing the cool water to increase its temperature and the hot water to decrease its temperature. This process repeats until the entire mixture reaches thermal equilibrium.
Convection occurs in our atmosphere all the time. On hot summer days, the ground is heated up by the sun (in a process that will be discussed in the next section of this video). The air directly above the ground heats up due to conduction, and then the convection process causes that heat to rise up into the atmosphere. This causes a lot of vertical motion in the air.
This is why, in the summer time, we tend to see a lot of cumulus clouds, which have a lot of vertical height to them. They occur when there is a lot of convection in the atmosphere. Atmospheric convection also causes turbulence in airplanes.
Convection doesn’t happen as much in the winter, because the ground doesn’t heat up as much when it’s covered in snow. Winter days tend to cause stratus clouds, which are very flat, indicating that there isn’t a lot of convection, or vertical motion, in the atmosphere.
The third type of heat transfer is known as electromagnetic radiation. This is heat that is transferred from one place to another through light waves. Heat from the sun is capable of travelling nearly 150 million kilometers through the vacuum of space to our planet as light waves. When those light waves reach the surface of the Earth, the objects the light hits will heat up.
The amount that objects heat up has to do with how much of the light they absorb. Black objects absorb all of the visible wavelengths of light, which is why they appear to be black. This absorption makes black objects heat up much more readily than objects of a different color.
This may be something you experience if you have a dark colored car. The sun’s light is absorbed by the car, heating it up. This is very nice in cold weather, but can make it hard to cool the car down in hot weather. If you drive a white or silver car, very likely you have the opposite experience. Your car remains cooler in hot weather, but does not heat up as much from the sun’s rays in the cold.
To demonstrate this, I’ve placed temperature probes in otherwise identical cans. The only difference between the two cans is that one is silver, and the other has been painted black. I connected the temperature probes to Logger Pro and turned on a heat lamp. The heat lamp was placed so that it was equidistant from both cans. Right away, the black can starts recording higher temperatures, indicating that it heats up more readily from electromagnetic radiation due to its color. The silver can heats up, but not as quickly.
If a black object heats up faster, what can we say about how quickly it cools down? I removed the heat lamp and recorded the temperature of both cans as they cooled off. The black can not only heats up faster, but also cools down faster as well.
The sun is not the only object that emits electromagnetic radiation. In fact, when the cans cool down, they are actually re-emitting that electromagnetic radiation into the air and surrounding objects. Humans also absorb and emit electromagnetic radiation. The reason we don’t see it is that the wavelengths of light we emit are in the infrared. Infrared light is not something that the human eye is able to see.
If we use an infrared camera, we can collect infrared light that is emitted from different objects. This is an infrared photo of one of the COD physics classes from a few years ago. Notice that people, which are warm compared to the air, emit a good amount of infrared light, which is then collected by the camera.
The students who wear glasses look like they have dark spots around their eyes. This is because glass does not allow infrared light to pass through it. It’s not that the students have cold eyes… it’s that the infrared radiation emitted by the student’s eyes is blocked from reaching the camera.
The hotter an object is, the higher the energy of the light that they will emit. Infrared has relatively low energy and is generally cool, as are humans. Things that are very hot, such as stars, are much hotter and emit higher energy light. Light with more energy than infrared is red light, orange light, all the way to blue light and then ultraviolet. A blue star would therefore be much hotter than a red star. We’ll revisit these topics when we talk about electromagnetic waves in lecture 26.
In general, if an object absorbs more energy than it emits, it will heat up. If an object emits more energy than it absorbs, it will cool down.
The greenhouse effect
The greenhouse effect describes what happens when an object absorbs more energy than it emits. A greenhouse can be something very beneficial, in the case of an actual greenhouse, which is used to keep plants from dying off in cold weather. In the case of our planet acting as a greenhouse, warming up the atmosphere and contributing to global climate change, the greenhouse effect is decidedly less positive.
First, let’s discuss what the greenhouse effect actually is. A greenhouse is generally a glass building filled with plants. Sunlight is able to enter into the greenhouse through the windows, and the heat from that light is absorbed by the plants. The plants will re-emit light. Because plants are relatively cool, they emit heat as infrared light. As we saw from that infrared photo, infrared cannot transmit through glass. Instead, it gets reflected off of glass surfaces. This means that all of the heat from the plants is trapped inside the greenhouse, causing the greenhouse to stay warm even if the outside is cold.
In this demo, two otherwise identical transparent plastic bottles have been placed at equal distances from a heat lamp. One of the plastic bottles has been filled with carbon dioxide, a greenhouse gas. As the heat lamp shines on both of the bottles, the temperature recorded by the computer shows that the bottle filled with carbon dioxide warms up much faster.
Globally, the greenhouse effect is an issue for our planet as our atmosphere contains a lot of carbon dioxide and other greenhouse gasses that have accumulated in large quantities due to human activities. As our planet continues to warm up, this becomes a bigger and bigger problem.
To a certain extent, the fact that our planet is capable of trapping heat makes it possible for our planet to sustain life. It’s when this problem causes our atmosphere to heat up to dangerous levels, that leads to catastrophic weather events. This is an area where technology and policy need to come together to create lasting change that will protect our planet and its inhabitants.
Engineering heat transfer
Now that we know how heat is moved around from one place to another, how could we use that knowledge to engineer a container that can keep hot things hot, or cold things cold?
A thermos or other type of insulated beverage container is a great example of this. A thermos is made from a double-walled material. Inside the two walls is a vacuum. The inside of the thermos is silver in color. To keep things hot, or cold, we put a lid on top. How do all of those features keep our hot things hot and our cold things cold?
First, let’s answer the question of “how does a Thermos know if something is hot, and should keep it hot, or if something is cold, and should keep it cold?” The answer is that those two concepts are identical. To keep something hot, we want to prevent heat from leaving the object. To keep something cold, we want to prevent heat from entering the object. Either way, we’re eliminating or reducing all opportunities for heat transfer to occur.
To eliminate or reduce heat conduction, the vacuum in the thermos walls prevents heat from entering or leaving through the walls of the container. Gas in general is a bad heat conductor, and vacuum is incapable of conducting heat, as there are no molecules to bump into to move heat around. A thermos lid is usually made of a heat insulator: maybe plastic or cork.
To eliminate or reduce convection, the vacuum between the thermos walls is also incapable of convecting. Because there are no molecules in a vacuum, they cannot distribute heat by moving around. By placing a lid on the thermos, we are eliminating convection in the vertical direction by trapping heat inside the thermos.
Finally, the silver color of the thermos eliminates electromagnetic radiation. Any heat inside the thermos is going to reflect off the walls and stay inside. Any heat outside of the thermos is going to reflect off the walls and stay outside.
In this demo, I have placed hot water at the starting temperature of 90 degrees Celsius into a double-walled calorimeter, and a metal can, the same used on the inside of the calorimeter, this one without a lid. The calorimeter acts the most like a thermos. There are two silver cups surrounded by air (not a good heat conductor), and a plastic and cork lid prevents convection.
After placing the hot water into both containers, I recorded the temperature changes as they cooled down. Over a span of ten minutes, the double-walled calorimeter held heat much better than the open metal can did. Much of the heat in the metal can was lost due to convection. Even placing a lid on a pot, pan, or your favorite coffee mug, will help keep your food and beverages warmer for a longer time.
The Earth is constantly receiving energy from the sun. Solar power can be used to generate electricity for use in our homes using a photovoltaic panel, known as a solar panel.
In this demo, a solar panel is connected to an LED. When no light is shining onto the solar panel, there is no electricity generated, and the LED remains off. Once I shine a flashlight onto the solar panel, electricity is generated and the LED turns on. This is a similar process to what happens when sunlight shines onto solar panels connected to your home or to the power grid.
The rate at which we obtain that energy is known as power: solar power. In general, the sun transmits 1,400 Joules of energy every second to every square meter that it hits. In other words, we receive 1,400 Watts per meter squared. This value is known as the solar constant.
If we consume a certain amount of power, we can use that information to determine how large of a solar panel we would need to generate that amount of electricity. Our power needs must be equal to the power we receive from the sun. In other words: what we need is equal to what we get.
The amount of power we need depends on how much we run our appliances. On average, a household in the United States consumes 1,250 Watts of power in one day. So what we need is equal to 1,250 Watts. What we get is going to be equal to the solar constant, 1,400 Watts per meter squared times the area of the solar panels. Dividing both sides of the equation by 1400 Watts per meter squared, we can calculate the area of the solar panel to be 0.89 square meters.
Sounds good, right? But solar panels aren’t necessarily 100% efficient. A good solar panel is at best 15% efficient as of the time I recorded this lecture video. How does this change our equation? What we need is still 1,250 Watts. But now what we GET is the solar constant times the area times the efficiency. So 1250 Watts equals 1400 Watts per square meter times 0.15 times the area. When we multiply 1400 Watts per square meter times 0.15 we get 210 Watts per square meter, which is how much power from the sun is converted into actual energy using our solar panels. Divide both sides by 210 and we see that the area of our solar panels would need to be 5.95 square meters. That’s a big difference!
Making solar panels more efficient is a big topic in engineering and physics research. More efficient solar panels will make renewable energy much more competitive than fossil fuels, and more convenient.
Another factor we must consider, if we do not live at the equator, is that the amount of energy we receive from the sun is going to change throughout the seasons. This is because the sun does not necessarily hit all parts of the surface of the Earth at a direct 90 degree angle. The equator may receive that 90 degree light, which gives that nice solar constant of 1400 Watts per square meter, but any part of the Earth tilted away from the sun will not.
In the northern hemisphere in summer, the Earth’s axis is tilted toward the sun, providing us with more direct light. We therefore obtain more energy from the sun, and the northern hemisphere climate warms up, giving us hot summers. In the winter, the Earth’s axis is tilted away from the sun, providing us with less direct light. We obtain less energy from the sun, and the northern hemisphere climate cools down, giving us cold winters.
Newton’s law of cooling
Newton’s law of cooling defines the rate at which an object loses heat, or cools down. It states that the change in temperature over time: delta T (big T for temperature) divided by delta t (little t for time), is proportional to the temperature of an object minus the temperature of the surroundings.
That means when there’s a big temperature difference between an object and its surroundings, we will expect it to cool down quickly. But as it cools down, the temperature difference between the object and the surroundings decreases, causing the rate of cooling to decrease as well. This continues to decrease until the temperature of the object asymptotically reaches the temperature of the surroundings.
This type of relationship is known as a differential equation and is described by a function known as an exponential function. We won’t go into the details of the math of this function, but we will use the basics to understand and interpret a graph of the cooling of an object.
I took water at an initial temperature of 94 degrees Celsius and recorded the temperature change over time as it cooled down. The temperature of the room was also recorded at a constant value of 22.5 degrees Celsius. The temperature recordings were measured for ten minutes.
After the experiment was completed, I was able to use Logger Pro to calculate the exponential equation that represented the data. I’m using it here to extrapolate the data so we could see what trend would occur if the experiment had been performed for an entire hour.
At the very beginning of the experiment, the temperature of the water was 94 degrees and the temperature of the room was 22.5 degrees. The difference in temperature was 71.5 degrees Celsius. At that time, the rate of cooling is 2.9 degrees C per minute. That is, the slope of the line at this instant in time says that the water will cool off at this rate. Because the function isn’t a straight line, that slope is constantly changing, but it’s valid at this particular data point.
At 7.2 minutes into the experiment, the water had cooled down to 76.1 degrees Celsius. Now the temperature difference is 53.6 degrees C, three-quarters of the initial value. What we should expect is that the slope of the line at this point will also be three-quarters of 2.9 degrees C per minute, and it is, it’s 2.1 degrees C per minute.
We can look at a few more points and see that this trend is satisfied for all of the data calculated in this experiment. 17.3 minutes in, we would expect the temperature of the water to be 58.3 degrees C, causing a difference in temperature to be 35.8 degrees C, one half the original value. Now the slope of the line at this point is one half the original value, 1.4 degrees C per minute.
Finally, 34.6 minutes in to the experiment, the temperature of the water would be 40.4 degrees C, causing the temperature difference to be 17.9 degrees C, one quarter of the initial value. The slope is now one quarter the initial slope, which is now 0.7 degrees C per min.
That slope continues to decrease over time. That is to say, as the water gets closer to room temperature, it cools down slower and slower, until eventually it asymptotically reaches the temperature of the room and is in thermal equilibrium.
Thanks for taking the time to learn about heat transfer! Until next time, stay well.