The first law of thermodynamics thinks big: it deals with the total amount of energy in the universe, and in particular, it states that this total amount does not change. Put another way, the First Law of Thermodynamics states that energy cannot be created or destroyed. It can only be change form or be transferred from one object to another.
This law may seem kind of abstract, but if we start to look at examples, we’ll find that transfers and transformations of energy take place around us all the time. For example:
Importantly, none of these transfers is completely efficient. Instead, in each scenario, some of the starting energy is released as thermal energy. When it’s moving from one object to another, thermal energy is called by the more familiar name of heat. It’s obvious that glowing light bulbs generate heat in addition to light, but moving pool balls do too (thanks to friction), as do the inefficient chemical energy transfers of plant and animal metabolism. To see why this heat generation is important, stay tuned for the Second Law of Thermodynamics.
An object’s energy can be converted from one form to another.
For instance, let’s consider our favorite example, the wrecking ball.
As the wrecking ball hangs motionless several stories up, it has no kinetic energy, but a lot of potential energy. Once it is released, its kinetic energy begins to increase because it builds speed due to gravity, while its potential energy begins to decrease, because it is no longer as far from the ground. Just before it hits the ground, the ball has almost no potential energy and a lot of kinetic energy.
The same kinds of conversions are possible with chemical energy, and we see lots of examples of this in our day-to-day lives.
Energy can change forms in a similar way in living organisms.
What is conservation of energy?
What is the principle of conservation of energy?
In physics, the term conservation refers to something which doesn’t change. This means that the variable in an equation which represents a conserved quantity is constant over time. It has the same value both before and after an event.
There are many conserved quantities in physics. They are often remarkably useful for making predictions in what would otherwise be very complicated situations. In mechanics, there are three fundamental quantities which are conserved. These are energy, momentum and angular momentum.
If you have looked at examples in other articles—for example, the kinetic energy of charging elephants—then it may surprise you that energy is a conserved quantity. After all, energy often changes in collisions. It turns out that there are a couple of key qualifying statements we need to add:
• Energy, as we’ll be discussing it in this article, refers to the total energy of a system. As objects move around over time, the energy associated with them—e.g., kinetic, gravitational potential, heat—might change forms, but if energy is conserved, then the total will remain the same.
• Conservation of energy applies only to isolated systems. A ball rolling across a rough floor will not obey the law of conservation of energy because it is not isolated from the floor. The floor is, in fact, doing work on the ball through friction. However, if we consider the ball and floor together, then conservation of energy will apply. We would normally call this combination the ball-floor system.
In mechanics problems, we are likely to encounter systems containing kinetic energy (EK), gravitational potential energy (Ug), elastic—spring—potential energy (Us), and heat (thermal energy) (EH). Solving such problems often begins by establishing conservation of energy in a system between some initial time—subscript i—and at some later time—subscript f.
EKi+Ugi+Usi=EKf+Ugf+Usf+Ehf
Which could be expanded out as:
12mvi2+mghi+12kxi2=12mvf2+mghf+12kxf2+EHf
What do we mean by system here?
In physics, system is the suffix we give to a collection of objects that we choose to model with our equations. If we are to describe the motion of an object using conservation of energy, then the system should include the object of interest and all other objects that it interacts with.
In practice, we always have to choose to ignore some interactions. When defining a system, we are drawing a line around things we care about and things we don’t. The things we don’t include are usually collectively termed the environment. Ignoring some of the environment will inevitably make our calculations less accurate. There is no indignity in doing this however. In fact, being a good physicist is often as much about understanding the effects you need to describe as it is about knowing which effects can be safely ignored.
Consider the problem of a person making a bungee jump from a bridge. At a minimum, the system should include the jumper, bungee, and the Earth. A more accurate calculation might include the air, which does work on the jumper via drag, or air resistance. We could go further and include the bridge and its foundation, but since we know that the bridge is much heavier than the jumper, we can safely ignore this. We wouldn’t expect the force of a decelerating bungee jumper to have any significant effect on the bridge, especially if the bridge is designed to bear the load of heavy vehicles.
There is always some tenuous level of interaction between even distant objects, so we need to choose the boundary of our system intelligently.
What is mechanical energy?
Mechanical energy, EM, is the sum of the potential energy and kinetic energy in a system.
EM=EP+EK
Only conservative forces like gravity and the spring force that have potential energy associated with them. Nonconservative forces like friction and drag do not. We can always get back the energy that we put into a system via a conservative force. Energy transferred by nonconservative forces however is difficult to recover. It often ends up as heat or some other form which is typically outside the system—in other words, lost to the environment.
What this means in practice is that the special case of conservation of mechanical energy is often more useful for making calculations than conservation of energy in general. Conservation of mechanical energy only applies when all forces are conservative. Luckily, there are many situations where nonconservative forces are negligible, or at least a good approximation can still be made when neglecting them.
How can conservation of energy describe how objects move?
When energy is conserved, we can set up equations which equate the sum of the different forms of energy in a system. We then may be able to solve the equations for velocity, distance, or some other parameter on which the energy depends. If we don’t know enough of the variables to find a unique solution, then it may still be useful to plot related variables to see where solutions lie.
Consider a golfer on the moon—gravitational acceleration 1.625 m/s2—striking a golf ball. By the way, Astronaut Alan Shepard actually did this. The ball leaves the club at an angle of 45∘ to the lunar surface traveling at 20 m/s both horizontally and vertically—total velocity 28.28 m/s. How high would the golf ball go?
We begin by writing down the mechanical energy:
EM=1/2mv2+mgh
Applying the principle of conservation of mechanical energy, we can solve for the height h—note that the mass cancels out.
1/2mvi2=mghf+1/2mvf2
h=12vi2−12vf2g=12(28.28 m/s)2−12(20 m/s)21.625 m/s2=123 m
How did we know the final speed was 20 m/s?
At the peak height, the vertical component of the velocity becomes zero. This means the only component of velocity at the peak height is the horizontal component. But since the horizontal component of the projectile doesn’t change during the flight, we can say that the horizontal component of the velocity—20 m/s—is equal to the total speed at the peak height.
As you can see, applying the principle of conservation of energy allows us to quickly solve problems like this which would be more difficult if done only with the kinematic equations.
Exercise 1: Suppose the ball had an unexpected collision with a nearby american flag hoisted to a height of 2 m. How fast would it be traveling at the time of collision?
Show solution.
1/2mvi2=mghf+1/2mvf2
vf=v2i–2⋅g⋅h−−−−−−−−√=28.16 m/s
Exercise 2: The image below shows a plot of the kinetic, gravitational potential and mechanical energy over time during the flight of a small model rocket. Points of interest such as maximum height, apogee, and the time of motor stop, burnout, are noted on the plot. The rocket is subject to several conservative and nonconservative forces over the course of the flight. Is there a time during the flight when the rocket is subject to only conservative forces? Why?
Energy transfer during the flight of a small model rocket [1].
Show solution.
The principle of conservation of mechanical energy tells us that if a system is only subject to conservative forces then the mechanical energy is constant. This is true for the period of the flight from 2.5 to 4 seconds. We can see that the mechanical energy curve is close to flat during this time. During this time, the rocket is coasting upwards—motor has stopped burning—but going slow enough that the work being done by drag on the rocket is mostly negligible.
Why can perpetual motion machines never work?
The perpetual motion machine is a concept for a machine which continues its motion forever, without any reduction in speed. An endless variety of weird and wonderful machines have been described over the years. They include pumps said to run themselves via their own head of falling water, wheels which are said to push themselves around by means of unbalanced masses, and many variations of self-repelling magnets.
Though often interesting curiosities, such a machine has never been shown to be perpetual, nor could it ever be. In fact, even if such a machine were to exist, it wouldn’t be very useful. It would have no ability to do work. Note that this differs from the concept of the over-unity machine, which is said to output more than 100% of the energy put into it, in clear violation of the principle of conservation of energy.
From the most basic principles of mechanics, there is nothing that strictly makes the perpetual motion machine impossible. If a system could be fully isolated from the environment and subject to only conservative forces, then energy would be conserved and it would run forever. The problem is that in reality, there is no way to completely isolate a system and energy is never completely conserved within the machine.
It is possible today to make extremely low friction flywheels which rotate in a vacuum for storing energy. Yet, they still lose energy and eventually spin down when unloaded, some over a period of years. The earth itself, rotating on its axis in space is perhaps an extreme example of such a machine. Yet, because of interactions with the moon, tidal friction, and other celestial bodies, it too is gradually slowing. In fact, every couple of years, scientists have to add a leap second to our record of time to account for variation in the length of day.
What is the first law of thermodynamics?
Learn what the first law of thermodynamics is and how to use it.
What is the first law of thermodynamics?
Many power plants and engines operate by turning heat energy into work. The reason is that a heated gas can do work on mechanical turbines or pistons, causing them to move. The first law of thermodynamics applies the conservation of energy principle to systems where heat transfer and doing work are the methods of transferring energy into and out of the system. The first law of thermodynamics states that the change in internal energy of a system ΔU equals the net heat transfer into the system Q, plus the net work done on the system W. In equation form, the first law of thermodynamics is,
ΔU=Q+W
Wait, why did my book/professor use a negative sign in this equation?
We have to be very careful with the first law. About half of textbooks, teachers, and professors write the first law of thermodynamics as ΔU=Q+W and the other half write it as ΔU=Q−W.
Both equations are correct, and they say the same thing. The reason for the difference is that in the formula ΔU=Q+Won gas, we are assuming that W represents the work done on the system, and when we use ΔU=Q−Wby gas we are assuming that W represents the work done by the system.
The two different equations are equivalent since,
Won gas=−Wby gas
When work is done on a system, the work done adds to the internal energy of the system (hence the plus sign in ΔU=Q+Won gas). When work is done by a system, the work done takes away from the internal energy of the system (hence the minus sign in ΔU=Q−Wby gas).
We’re going to use the equation ΔU=Q+Won gas with the plus sign on the work since that’s the one used by the College Board AP physics 2 exam. This means that when we write W, we will mean work done on the gas
Here ΔU is the change in internal energy U of the system. Q is the net heat transferred into the system—that is, Q is the sum of all heat transfer into and out of the system. W is the net work done on the system.
So positive heat Q adds energy to the system and positive work W adds energy to the system. This is why the first law takes the form it does, ΔU=Q+W. It simply says that you can add to the internal energy by heating a system, or doing work on the system.
What do each of these terms (ΔU,Q,W) mean?
Nothing quite exemplifies the first law of thermodynamics as well as a gas (like air or helium) trapped in a container with a tightly fitting movable piston (as seen below). We’ll assume the piston can move up and down, compressing the gas or allowing the gas to expand (but no gas is allowed to escape the container).
The gas molecules trapped in the container are the “system”. Those gas molecules have kinetic energy.
Can a gas molecule have potential energy?
Yes. Gas molecules can also have potential energy. Although we typically neglect the small change in gravitational potential energy due to the small changes in height of the gas in a container, a diatomic molecule like O2 can have a potential energy associated with the oxygen atoms vibrating toward and away from each other, somewhat like two masses connected by a spring. This vibration “mode” of energy is typically not significant until temperatures get much higher than room temperature. At room temperature there simply isn’t enough energy to get the atoms in a diatomic molecule to vibrate much.
Since most of the energy of a gas at reasonable temperatures will be in the form of kinetic energy, we can think of changes of internal energy as mostly being changes in the kinetic energy of the gas molecules (i.e. larger U means faster moving gas molecules).
The internal energy U of our system can be thought of as the sum of all the kinetic energies of the individual gas molecules. So, if the temperature T of the gas increases, the gas molecules speed up and the internal energy U of the gas increases (which means ΔU is positive). Similarly, if the temperature T of the gas decreases, the gas molecules slow down, and the internal energy U of the gas decreases (which means ΔU is negative).
It’s really important to remember that internal energy U and temperature T will both increase when the speeds of the gas molecules increase, since they are really just two ways of measuring the same thing; how much energy is in a system. Since temperature and internal energy are proportional T∝U, if the internal energy doubles the temperature doubles. Similarly, if the temperature does not change, the internal energy does not change.
One way we can increase the internal energy U (and therefore the temperature) of the gas is by transferring heat Q into the gas. We can do this by placing the container over a Bunsen burner or submerging it in boiling water. The high temperature environment would then conduct heat thermally through the walls of the container and into the gas, causing the gas molecules to move faster. If heat enters the gas, Q will be a positive number. Conversely, we can decrease the internal energy of the gas by transferring heat out of the gas. We could do this by placing the container in an ice bath. If heat exits the gas, Q will be a negative number. This sign convention for heat Q is represented in the image below.
Since the piston can move, the piston can do work on the gas by moving downward and compressing the gas. The collision of the downward moving piston with the gas molecules causes the gas molecules to move faster, increasing the total internal energy. If the gas is compressed, the work done on the gas Won gas is a positive number. Conversely, if the gas expands and pushes the piston upward, work is done by the gas. The collision of the gas molecules with the receding piston causes the gas molecules to slow down, decreasing the internal energy of the gas. If the gas expands, the work done on the gas Won gas is a negative number. This sign convention for work W is represented in the image below.
Below is a table that summarizes the signs conventions for all three quantities (ΔU,Q,W) discussed above.
| ΔU (change in internal energy) | Q (heat) | W (work done on gas) |
| is + if temperature T increases | is + if heat enters gas | is + if gas is compressed |
| is − if temperature T decreases | is − if heat exits gas | is − if gas expands |
| is 0 if temperature T is constant | is 0 if no heat exchanged | is 0 if volume is constant |
Is heat Q the same thing as temperature T?
Absolutely not. This is one of the most common misconceptions when dealing with the first law of thermodynamics. The heat Q represents the heat energy that enters a gas (e.g. thermal conduction through the walls of the container). The temperature T on the other hand, is a number that’s proportional to the total internal energy of the gas. So, Q is the energy a gas gains through thermal conduction, but T is proportional to the total amount of energy a gas has at a given moment. The heat that enters a gas might be zero (Q=0) if the container is thermally insulated, however, that does not mean that the temperature of the gas is zero (since the gas likely had some internal energy to start with).
To drive this point home, consider the fact that the temperature T of a gas can increase even if heat Q leaves the gas. This sounds counterintuitive, but since both work and heat can change the internal energy of a gas, they can both affect the temperature of a gas. For instance, if you place a piston in a sink of ice water, heat will conduct energy out the gas. However, if we compress the piston so that the work done on the gas is greater than the heat energy that leaves the gas, the total internal energy of the gas will increase.
What do solved examples involving the first law of thermodynamics look like?
Example 1: Nitrogen piston
A container has a sample of nitrogen gas and a tightly fitting movable piston that does not allow any of the gas to escape. During a thermodynamics process, 200 joules of heat enter the gas, and the gas does 300 joules of work in the process.
What was the change in internal energy of the gas during the process described above?
Solution:
We’ll start with the first law of thermodynamics.
ΔU=Q+W (start with the first law of thermodynamics)
ΔU=(+200 J)+W(plug in Q=+200 J)
Why is heat a positive number here?
Our convention is that the heat Q will be a positive number if heat enters the gas, since it increases the internal energy of the gas.
ΔU=(+200 J)+(−300 J) (plug in W=−300 J)
Why is work a negative number here?
The convention we use is that the work is a positive number if work is done on the gas, since that adds energy to the gas. But since in this problem work was done by the gas, we plug in a negative number for the work done, since this subtracts energy from the gas.
ΔU=−100 J
Note: Since the internal energy of the gas decreases, the temperature must decrease as well.
Example 2: Heating helium
Four identical containers have equal amounts of helium gas that all start at the same initial temperature. Containers of gas also have a tightly fitting movable piston that does not allow any of the gas to escape. Each sample of gas is taken through a different process as described below:
Sample 1: 500 J of heat exits the gas and the gas does 300 J of work
Sample 2: 500 J of heat enters the gas and the gas does 300 J of work
Sample 3: 500 J of heat exits the gas and 300 J of work is done on the gas
Sample 4: 500 J of heat enters the gas and 300 J of work is done on the gas
Which of the following correctly ranks the final temperatures of the samples of gas after they’re taken through the processes described above.
A. T4>T3>T2>T1
B. T1>T3>T2>T4
C. T4>T2>T3>T1
D. T1>T4>T3>T2
Solution:
Whichever gas has the largest increase in internal energy ΔU will also have the greatest increase in temperature ΔT (since temperature and internal energy are proportional). To determine how the internal energy changes, we’ll use the first law of thermodynamics for each process.
Process 1:
ΔU=Q+WΔU=(−500 J)+(−300 J)ΔU=−800 J
Process 2:
ΔU=Q+WΔU=(+500 J)+(−300 J)ΔU=+200 J
Process 3:
ΔU=Q+WΔU=(−500 J)+(300 J)ΔU=−200 J
Process 4:
ΔU=Q+WΔU=(+500 J)+(+300 J)ΔU=+800 J
The final temperatures of the gas will have the same ranking as the changes in internal energy (i.e. sample 4 has the largest increase in internal energy, so sample 4 will end with the largest temperature).
ΔU4>ΔU2>ΔU3>ΔU1 and T4>T2>T3>T1
So the correct answer is C.
– [Voiceover] Let’s now explore the first law of thermodynamics. And before even talking about the first law of thermodynamics, some of you might be saying, “Well, what are thermodynamics?” And you could tell from the roots of this word. You have thermo, related to thermal, it’s dealing with temperature. And the dynamics, the properties of temperature, how do they move, how does temperature behave? And that’s pretty much what thermodynamics is, it’s about, it’s the study of heat and temperature, and how it relates to energy and work, and how different forms of energy can be transferred from one form to another. And that’s actually the heart of the first law of thermodynamics which we touched on on the introduction to energy video. And the first law of thermodynamics tell us that energy, this is an important one, I’m going to write it down, energy cannot be created or destroyed. Cannot be created, or destroyed. It can only be converted from one form to another. It can only only be converted only be converted, I’m having trouble writing today. Converted from one form, from one form, to another. Or you could transfer it but you’re not going to, you’re not going to create or destroy it. And the whole thing that I, the rest of this video I just want to really have you internalize that, and I want to look at a bunch of examples and think about, well, what is the energy that we’re observing, or that we’re seeing in a system? And then thinking about where is that energy coming from, to appreciate that it’s not just coming out of nowhere, and that it’s not just disappearing, it’s not getting destroyed either. And so let’s start with this example of a lightbulb. And I encourage you to pause this video, think about the forms of energy that we can see here, and then think about where is that energy coming from, and where is it going? Well, the most obvious form of energy that you see here, and this, the whole point of a lightbulb, is you see the radiant energy, you see the you see the electromagnetic waves, the light, being emitted from it. And that light, so this is radiant energy. Radiant energy. And that radiant energy, is due to the heat in the filament right over here, as the electrons go through it, it generates heat, so you have thermal energy. So you have thermal energy as well. Thermal energy. But where does this radiant and thermal energy come from? Again, first law of thermodynamics it tells us, it’s not just being created out of thin air, it must be converted or being transferred from some place. Well, I just gave you a hint, this thermal energy is due to the electrons moving through the filament. They’re moving through the filament which has some resistance, and that generates heat. So the electrons are moving through this, and as they move through that resistor, they generate heat. So you actually have the kinetic energy of the electrons. I’ll just write KE for short, kinetic energy of the actual electrons. Well, where is that kinetic energy coming from? Well that’s coming from the potential energy. You know maybe this thing is plugged into, is plugged into a socket of some kind. So let me draw a little electric socket right over here. And the electric socket, I’ll draw, the electric socket if this is the electric socket in your home, there is an electrostatic potential between these two terminals. And so when you make a connection, the electrons are able to move. And we’ll get into the details of AC and DC current in the future, but there’s an electrostatic potential, from this point to this point if we assume that’s the direction that the electrons are going in. And so that, it’s that potential energy we convert to this kinetic energy of the electrons, which is really in the form of a current, and then that gets converted into thermal energy and radiant energy. Now what happens after, let’s say you unplug the light, the light goes dark, what happened to all of that energy? Is it still there? Well yeah, that thermal energy is going to continue to dissipate through the system. And this right over here would be an open system, it’s going to, the air inside the lightbulb, you can’t fully see the lightbulb right here, but it looks something like this. That’s going to heat up, but then it’s going to heat up the glass surrounding the lightbulb, and that’s going to heat up the surrounding air. So the thermal energy is going to be transferred, and that radiant energy is going to move outward. And it could be used, it could be converted into other forms of energy, most likely thermal energy, it is also probably going to heat up other things. Well, what about a pool table? When I hit a, if I hit a pool, a billiard ball or a pool ball right over here, well, where is that energy going? Well some of that energy might be going to go hit the next ball, which might go to hit the next ball. But as we all know, if we’ve ever played pool, at some point they’re going to stop. So what happened to all of that energy? Well, while they were rolling, there was some air resistance, so they’re bumping against these, the air molecules, and it’s really friction due to air. And that energy is essentially going to be converted to heat. And one trend that you’re going to see very frequently, is as systems progress, a lot more of the energy tends to turn into heat, rather than doing useful work. And so you’re going to have, as the billiard balls move, there’s the air, and so that’s going to be, that’s going to be converted, some of that kinetic energy is going to be turned into heat energy. You’re also going to have friction with the actual felt on the table. And that friction, you’re going to have molecules rubbing up against each other, that’s also going to be converted into heat. And so that, because that kinetic energy gets sapped off, gets keeping sapped away from the friction, which is essentially converting the kinetic energy to heat energy, eventually you won’t have any more kinetic energy. Now what about this weight lifter here? He’s using the chemical energy in his, in the ATP in his muscles, that converts into kinetic energy that moves his muscles, that moves this weight, but once he’s in this position, what happened to all of that energy? Well, a lot of that energy is now being stored in potential. it’s the potential energy, he’s got this big weight, he’s got that big weight above his head, and if he were to just let go, that thing would fall, I wouldn’t recommend he do that, but that thing would fall quite fast. And so now it’s all, or a lot of it has been stored up in potential energy. But he would have also generated heat, his muscles would have generated heat. Even the act of moving it through the air is going to be some heat in the air, some friction with it. And so I want you to appreciate that this energy is not coming out of nowhere, it is being converted from one form or another, or being transferred from one part of the system to another. Now we can look at these examples over here. Same thing with our runner, what happens after, you can buy the fact that okay, his chemical energy is allowing his muscles to move, and that’s turning in his kinetic energy for his entire body, his body is moving, but at some point he stops, where did all that energy go? Well, some of it will be heat in his body that’s being dissipated into the broader system, into the air. And also, when he was running, there was this contact with the ground, that’s going to make the molecules of the ground vibrate a little bit, some of it will be transferred as sound, so the air particles moving through the air, and a lot of it will be heat. And we’re going to see that over and over and over again. The diver up here, you have mostly potential energy. Then it converts to kinetic energy as he’s, as he gets almost in the water. But what happens once he falls into the water? Well, then that energy’s going to be transferred, as you’re going to have these waves of water move away. And it will also increase friction, so, well actually he would have had friction as he fell down, so that would have generated some heat, and there would have been also some heat with the friction with the water, you normally don’t think of friction with the water, but there is some friction with the actual water, and there’s also, these waves, you have higher kinetic energy of the actual water being transferred outward from where he actually dropped in. And I could keep going on and on. You have the chemical potential energy of the fuel here being, you have combustion occurring, and then that gets converted into the thermal energy, and the radiant energy of what we associate with fire. And that doesn’t disappear, it just keeps radiating outwards, the radiant energy just keeps radiating outward, maybe it might heat up something. And the thermal energy will just keep radiating outward, or I should say, the thermal energy will just dissipate outward, and heat up the things around it. Same thing with our lightning example. You start with the electrostatic potential, where the bottom of the clouds were more negative, and then the ground is positive as well, and at some point, that potential energy turns into kinetic energy as the electrons transfer through the air, and then that gets converted into, or a good bit is going to be converted to heat and radiant energy. So the whole point of this video is, no matter what example you look at, if you think about it carefully enough, and I encourage you to do this in your everyday life, the energy isn’t just coming out of, you know, magically appearing, it’s just being converted from one form to another.