Hello there! Welcome to lecture 15: temperature and heat!
Temperature and heat are important phenomena that start to unlock the ideas of thermodynamics, which we’ll be focusing on in the next few lectures. Temperature is something that impacts our lives greatly as we move throughout the seasons. We’ll see where the temperature scales that we use come from and how temperature is measured.
Our discussion will then turn to heat and how easy, or hard, it is to change the temperature of different substances. This helps us to understand climate and cooling systems, among other things.
Finally, we’ll discuss thermal expansion. Thermal expansion has far-ranging implications from the existence of aquatic life on this planet, to understanding how objects change their sizes from month to month as temperatures change.
Each of the following concepts will be discussed in this video: temperature, heat, specific heat capacity, and thermal expansion.
Temperature defines the average kinetic energy of an object. It quantifies the “hotness” or “coldness” of something. The symbol for temperature is the uppercase letter T. We’ll discuss the units we use to describe temperature in a few minutes.
From a human perspective, temperature is extremely important in helping us determine what to wear when we go outside, and in deciding on what types of indoor and outdoor activities we want to do. Having an objective temperature scale is important in that it cuts out the subjective interpretation of each person’s idea of what may be “hot” or “cold”. From a physics perspective, an objective temperature scale enables scientists to perform experiments on thermodynamics, climate change, and other important phenomena.
Let’s look at an example of how temperature is related to the average kinetic energy of a substance. In lecture seven, we learned that kinetic energy describes the energy of motion. Therefore, it would be reasonable to expect that a substance at a higher temperature will have more motion than a substance at a lower temperature.
In this demo, I have two beakers. The one on the left is filled with cold water, and the one on the right is filled with hot water. Just a note, the beaker on the left appears translucent due to the fact that water vapor from the air has condensed on it. We’ll talk about that phenomenon in chapter seventeen.
A drop of blue food dye is dropped into each beaker. After watching for several moments, you can see the food dye swirl around and distribute itself much more rapidly in the beaker of hot water, demonstrating its motion is much greater than that of the cold water.
Now that we understand what temperature is, we need a way to measure it. There are two types of temperature scales that can be used, empirical scales and absolute scales.
Let’s talk about empirical scales first. An empirical scale just means that experiments were performed to derive the upper and lower limits of the scale. The Fahrenheit scale was proposed in the 1700s. The limit for the cold end of the temperature scale was chosen as a frozen salt water solution. That temperature was denoted as zero. The limit for the hot end of the temperature scale was chosen as a human body temperature. This temperature was denoted at ninety. Eighty-nine gradations can be placed in between, creating the Fahrenheit temperature scale.
The Fahrenheit scale isn’t terribly scientific because it’s not repeatable. Let’s say I ask you to re-create the Fahrenheit scale. Depending on how much salt you place in your freezing salt water solution, and whether or not you’re sick with a fever, you may wind up with different definitions of 0 and 90 Fahrenheit. Even if we standardize how much salt to place in the water, we are still limited by the variations in human body temperature. While Fahrenheit is admittedly useful as a temperature scale, as we tend to experience the full range of temperatures from zero to one hundred, it’s not how scientists describe temperature.
The Celsius scale was also developed in the 1700s. The cold end of the temperature scale is established by the freezing point of water, and is called zero Celsius. The hot end of the temperature scale is established by the boiling point of water, and is called one hundred Celsius. 99 gradations can be placed in between to establish the temperature scale and allow us to measure temperatures in between those two extremes.
Celsius is a scientific scale because it’s repeatable. As long as you and I both start with pure water, and freeze and melt it at one atmosphere of pressure, we will both develop identical temperature scales. Because of this, Celsius is the scale that we will use, almost exclusively, to discuss temperature in this class.
Although we will not be using Fahrenheit in this class, it is still useful to understand how to convert from Fahrenheit to Celsius, and vice versa. First, we need to establish where the two scales overlap with each other. Zero Celsius is equal to thirty-two Fahrenheit. Then we need to know how much of a change in one scale relates to a change in the other scale. A change in one degree Celsius is equal to a change in 1.8 degrees Fahrenheit.
Therefore, to convert from Celsius to Fahrenheit, take the temperature in Celsius, multiply by 1.8, and add 32. The result will be the temperature in degrees Fahrenheit. As an example, 10 degrees Celsius converts to 50 degrees Fahrenheit.
To convert from Fahrenheit to Celsius, take the temperature in Fahrenheit and subtract 32 from it. Multiply the result of that subtraction by five-ninths. The result is the temperature in degrees Celsius. As an example, 86 degrees Fahrenheit converts to 30 degrees Celsius.
The other type of temperature scale that can be used is called an absolute scale. Absolute scales are designed by establishing the lower limit based on a physical limitation. As we will discuss in lecture 18, there is a lowest possible temperature that can be achieved. That limit is known as absolute zero. As far as we know, nothing can be colder than absolute zero. This establishes the lower limit of our absolute scale.
The absolute scale that’s used in physics is known as the Kelvin scale. The zero end of the Kelvin scale is absolute zero. Because there’s no upper limit to the temperature of an object, there is no hot end to the scale. How do we establish the gradations of each unit of Kelvin? The Kelvin scale was developed so that a change in one Kelvin is equal to a change in one degree Celsius.
Absolute zero is equal to -273 degrees Celsius. Therefore, to convert from Celsius to Kelvin, simply add 273. To convert from Kelvin to Celsius, subtract 273. Just a note to check your work: there is no such thing as a negative temperature in Kelvin, so if you get a negative answer when converting to Kelvin, check your math!
Kelvin is the established SI unit for temperature. However, we will mostly make use of Celsius in this class. At times, though, we will see that the use of Kelvin is required.
Now that we understand where temperature scales come from, we need to be able to measure temperature. We do so using a thermometer. Let’s build a thermometer to see how they work.
In this demo, I’ve attempted to create a thermometer based on the Celsius scale. In other words, the zero part of my scale will be established by the freezing point of water, and the one-hundred part of my scale will be established by the boiling point of water. My thermometer uses dyed water in a glass bulb with a tube that allows the liquid to expand.
First, I’d like to point out some really important drawbacks to this thermometer. Because it’s made out of water, I would expect the liquid inside to freeze when it reaches zero, which means that it wouldn’t make a very good thermometer anymore. When it reaches one hundred, I would expect that the water will boil, again, not a good property of a liquid inside a thermometer. But it still makes a good example.
First, I start by drawing a line on the glass tube indicating the water level at room temperature. Then, I take the glass bulb of my thermometer and place it into freezing cold water. The water contracts (a phenomenon I’ll talk about at the end of this lecture video). At a certain point, the water level will reach equilibrium. At that point, I can draw a line on the glass tube establishing the zero point of my thermometer.
Then, I place the glass bulb of my thermometer into boiling hot water. The water inside the thermometer vigorously expands. In fact, it expanded so much that it started coming out of the top of the tube! In order to make this thermometer work, I’d need to use a longer tube, or maybe a liquid that doesn’t expand as much.
Now, let’s say for the sake of argument that my thermometer was really rock solid and had a zero level established by the freezing water, and a one-hundred level just below the top of the tube. Then I can place 99 gradations in between. When I take my thermometer out and about with me, I can read off the level of the water to determine the temperature.
A good analog thermometer uses a substance that will remain liquid at most temperatures that the thermometer will be exposed to. In most modern thermometers, that liquid is dyed alcohol, which is able to remain in a liquid form throughout all temperatures that humans can reasonably expect to experience throughout the year.
Previously, thermometers were made out of mercury. Mercury remains liquid at a vast range of temperatures, but unfortunately is highly toxic. For that reason, it’s been phased out of most consumer devices.
A digital thermometer has a device inside whose electrical properties are changed as a function of temperature. The relationship between temperature and the electrical property are well known. Therefore, by measuring the electrical property, the temperature can be determined. A microcontroller then converts that temperature into numbers and displays them on an LCD screen.
Heat is energy that is transferred from one object to another in response to a difference in temperature. The symbol for heat is the uppercase letter Q. The units used for heat are calories, but because heat is a form of energy, we know that Joules will also work. In this class, we will mostly work with calories.
Heat only spontaneously flows from hot to cold, and never spontaneously flows in the opposite direction. To relate this to something more familiar, consider it to be similar to gravity. If a ball is placed at the top of a ramp, gravity will pull the ball downward, causing it to roll down the ramp. Once the ball reaches the bottom of the ramp, gravity will not pull it back up to the top again. The only way for the ball to reach the top of the ramp is for a person, animal, or machine, to exert energy in physically moving it back to the top again. Going against gravity requires work.
In much the same way, working against the established flow of heat takes work. Maybe you use a refrigerator or air conditioner. These seem to work against the flow of heat from hot to cold. And they do, but it requires energy to do this. If you’ve paid an electrical bill during a hot summer month when running the air conditioner, you know it’s not cheap to keep things cool. We’ll discuss the importance of this physical limitation of heat flowing spontaneously only from hot to cold in chapter eighteen.
The mechanisms through which heat can flow from one place to another will be the subject of our next lecture.
Specific heat capacity
Specific heat capacity is kind of like thermal inertia. It defines how difficult it is to change the temperature of a substance. The symbol for specific heat capacity is the lowercase letter c. The units are calories per gram degree Celsius. That tells us that specific heat capacity tells us how many calories of heat are required to increase (or decrease) the temperature of a certain mass of material by a certain amount.
An equation we can use that relates heat, specific heat capacity, mass, and change in temperature is Q = mc delta T. Q is the heat, measured in calories. M is the mass, measured in grams. C is the specific heat capacity. And delta T is the temperature change in degrees Celsius.
This equation only works when the temperature of a substance changes, and cannot be used when an item changes phase, for example to calculate the heat required to boil water. We’ll discuss the equation we can use in that case in lecture seventeen.
The specific heat capacity of water is 1 calorie per gram degree Celsius. This means I need one calorie of heat to raise the temperature of a single gram of water by one degree Celsius. This may not seem like a lot, but water actually has one of the highest specific heat capacities of common substances. It makes water a really good candidate for use in cooling systems, because it can absorb a lot of heat without changing its temperature very much. This fact also explains why the climate tends to be milder if you live near a large body of water. This could be an ocean, or even a large lake such as Lake Michigan. Because the water in an ocean or lake doesn’t change its temperature easily, it means that the water will act as a moderating influence as the seasons change. This also explains why daily temperature fluctuations are much larger in the desert than they are in wetter climates.
Let’s get some practice using the Q equals mc Delta T equation.
In this example, 347.6 grams of water was placed into a beaker, and then onto a pre-heated hotplate. The initial temperature of the water was 21.2 degrees Celsius. After a few minutes, the temperature increased to 44.9 degrees Celsius. We can calculate the amount of heat that enters the water due to the hotplate by using Q = mc Delta T. First, let’s calculate the change in temperature. Change is always equal to final minus initial. 44.9 minus 21.2 equals 23.7 degrees Celsius. Plugging the numbers in, we get that the heat equals 347.6 grams times 1 calorie per gram degree Celsius, times 23.7 degrees Celsius. The heat absorbed by the water is 8238.12 calories.
What happens if something cools down? Let’s say I take the beaker of water off of the hotplate and let it sit until it cools back down to room temperature. The mass is the same, the specific heat capacity is the same. But now the initial temperature would be 44.9 degrees Celsius and the final temperature would be 21.2 degrees Celsius. The change in temperature is NEGATIVE 23.7 degrees C. This means if I use Q = mc delta T, the result will be negative 8238.12 calories. The negative sign means that heat isn’t entering the substance, but leaving it.
In this second example, I have a beaker filled with 173.9 grams of copper and 364.3 grams of water mixed together. I can be reasonably certain that the two objects are in thermal equilibrium at the start of my experiment, as they were both mixed together for a while, and the thermometer gave a constant readout, indicating that both the copper and water were at the same initial temperature of 22.3 degrees Celsius.
After a few minutes of heating, the temperature of the mixture, which I’ve stirred around to ensure it’s in thermal equilibrium, has increased to 45.2 degrees Celsius. The change in temperature for both substances is 22.9 degrees Celsius.
How much heat enters the water and copper during that time? The good news is that we can look at both substances independently. That is, we can calculate how much heat enters the copper. Then we can calculate how much heat enters the water. Then we can add the two values together to find the total amount of heat that entered the mixture from the hotplate.
First, let’s use Q = mc Delta T for the water. 364.3 grams of water times 1 calorie per gram degree Celsius times 22.9 degrees Celsius is equal to 8342.47 calories of heat that enter the water. Next, let’s use Q = mc Delta T for the copper. The specific heat capacity of copper is 0.094 calories per gram degree Celsius. 173.9 grams times 0.094 times 22.9 degrees Celsius is equal to 374.34 calories of heat that enters the copper. Therefore, the total amount of heat entering the mixture is the sum of these two numbers, or 8716.81 calories.
That positive sign on our heat means that heat entered our mixture, causing it to increase in temperature. If we were to let the mixture cool down, we can anticipate that the heat will have a negative sign.
Both of those examples had one or more substance that were in thermal equilibrium with each other. That is, they both started and ended at the same temperature. But what happens if we mix two substances together, both starting out at different temperatures? What happens then? We can use conservation of energy to help us solve these questions. Assuming that no heat is lost to the environment, we know that if we take something hot and mix it with something cold, the heat that enters the cold substance is exactly equal to the heat that leaves the hot substance. In other words, Q hot plus Q cold equals zero.
Let’s say we were to mix together equal masses of water, one starting at 10 degrees Celsius, and the other starting at 50 degrees Celsius. Our intuition should tell us that the final temperature, once the mixture reaches thermal equilibrium, should be the average of the two temperatures, in this case, 30 degrees Celsius. That’s because the masses are equal and both substances are identical.
If the mass of the cold water increases, then the final temperature, in this example, will reside somewhere between 10 and 30 degrees C. If the mass of the hot water increases, then the final temperature will reside somewhere between 30 and 50 degrees C.
Either way, we can use Q hot plus Q cold equals zero to determine the final temperature of a mixture. This equation also works if the two substances are different from each other. Let’s consider an example where we have different masses of different substances at different starting temperatures and combine them together.
60 grams of aluminum, which has a specific heat capacity of 0.215 calories per gram degree Celsius, at an initial temperature of 80 degrees Celsius, is mixed with 200 grams of water at an initial temperature of 20 degrees Celsius. Neither the water nor the aluminum undergoes a phase change in this process. That is, the water remains liquid the whole time, and the aluminum remains a solid the whole time. After enough time has passed, the aluminum-water mixture has reached thermal equilibrium. What is the final temperature of that mixture?
Start with Q hot plus Q cold equals zero. The hot substance is aluminum, and the cold substance is water. Mass of hot times c of hot times Delta T of hot plus mass of cold times c of cold times Delta T of cold equals zero. Remember that Delta T is final minus initial. We know both of the initial temperatures of each substance, and we know that the final temperature will be the same for both the aluminum and the water because the mixture will be in thermal equilibrium.
Plug in the known values, and multiply. For the hot substance, distribute through the 12.9 calories per degrees C. For the cold substance, distribute through the 200 calories per degrees C. Then, combine like terms. Add 5032 calories to both sides of the equation. Then divide both sides of the equation by 212.9 calories per degree C to get T final by itself.
The final temperature of the mixture is 23.64 degrees Celsius. This makes sense based on our intuition. First, the final temperature is between 20 and 80, which is what we would expect. Second, there’s not only more water than aluminum, but it’s harder to change the temperature of water than aluminum, so it makes sense that the temperature is closer to the starting temperature of the water than it is to the starting temperature of the aluminum.
You will be using a process similar to this to derive the specific heat capacities of several metals in the lab on specific heat capacity and latent heat.
As we saw with the thermometer model, substances tend to expand when they are heated. Because the molecules within the object have more motion, it makes sense that most substances will expand when heated.
Let’s take a look at this in action. A metal ball and hoop start out at room temperature. The ball is easily able to pass through the hoop, demonstrating that the ball is smaller than the hoop’s opening. I heat up the ball with the blowtorch, which causes it to expand. It has expanded to such a degree that it is no longer able to fit through the hoop. Next, I heat up the hoop with the blowtorch. Because the hoop expands, now the ball is able to pass through again.
After the ball and hoop cool down again, they return to their original sizes.
Thermal expansion has some very important repercussions in our physical world. Notably, structural objects like bridges and buildings have to be engineered specifically while accounting for this expansion and contraction in hot and cold weather. Long bridges contain expansion joints. This enables them to stretch out in the heat without buckling or breaking.
Power lines also experience thermal expansion, sometimes in devastating ways. In the summer, power lines expand due to the heat. Not only that, but the load on the electrical lines also increases on hot days due to people using their air conditioning units. The excess load causes even more heat in the power lines, causing them to expand even more. If the expansion causes the power line to come into contact with tree limbs or a bush, then a short circuit can occur. In extreme cases, this may cause the power grid to go offline. In fact, this was one of the contributing causes to the Northeast Blackout of 2003, which caused my family’s home to be out of power for a week!
You may notice that tree limbs are trimmed around power lines. One reason for this is to prevent possible short circuits from occurring when the power lines sag.
It’s possible to engineer the thermal expansion of a material to be very similar to that of another substance. This is helpful for fillings we get in our teeth because of cavities. When we eat hot food, we want our teeth and the fillings inside of them to expand at the same rate. Composite fillings have been engineered to do just this.
What happens if two substances come together that have different rates of thermal expansion? Let’s take a look!
This video shows a bimetallic strip. That is, it’s made out of two different metals that are connected together. When I heat the bimetallic strip with a blowtorch, each metal expands at a different rate, causing it to curl up. The metal that expands more stretches out and experiences a tension force. The metal that expands less gets squished and experiences a compression force.
The bimetallic strip has found a practical application as an element in analog thermostats. A bimetal strip, when heated to a warm room temperature, will be coiled up. As the room cools down to a setpoint, the coil unfurls and eventually comes in contact with some type of sensor that sends a signal to the furnace to turn on and heat the room. Once the room heats up again, the metals coil up and deactivates the furnace. Similar bimetal coils are or have been used in refrigerators, computer cooling, and air conditioning systems.
While most substances expand when heated, not all of them do. A few substances will contract instead. This is known as negative thermal expansion. Notably, water is densest at four degrees Celsius. Below that temperature, water will expand. This is why ice cubes float on liquid water. It’s also why aquatic life is able to exist on our planet. Because ice floats, as long as a body of water is deep enough, the water at the bottom will be four degrees Celsius at the coldest time of year, enabling aquatic life to remain alive instead of freezing every winter. The ice also acts as an insulating layer, protecting the water below.
Whether objects expand or contract when heated, the molecules within the object need a sufficient amount of time to respond to these changes in size. Otherwise, it’s possible that the molecules inside an object will experience enough stress to cause them to break.
In this video, I start with a glass. There’s nothing wrong with it at the start, it’s a perfectly good glass. No scratches or defects at all. I heat the glass up with a blowtorch. Note that the glass stays intact, it just heats up. When I plunge the glass into a container filled with ice-cold water, the glass breaks. This is because the expansion and contraction isn’t given enough time to occur without causing huge amounts of stress in the glass. Thermal stress means that we have to be careful with the types of materials we use in and on our stoves and ovens. Specially tempered glass like Pyrex is used when wide swings of temperature are expected.
Thanks for taking the time to learn about temperature and heat! Until next time, stay well.