Energy
(If you want to skip my "capacity to cause pain" intro in which I imagine throwing things at you, you can jump down to "Let's make a law" below).
What is Energy?
This is trickier than it may seem, but it's very important that we have some understanding. One common definition is the capacity to do work. This begs the question: "what is 'work'?" Well, if you look that up, you find that work is a form of energy...that didn't help much.
I prefer to think of energy as "the capacity to cause pain." Yes, that's something of a joke, but it works better than you might think. Remember, the goal here is to come up with some way to relate things to each other. Pain is pain...we can all relate to it, no matter what causes it.
Imagine this: I'm standing before you with a spherical object I plan to throw at you; what are the things that matter to you? As the object is flying at your head, what determines how scared you are?
The units of pain
It's worth thinking about the units for this measure of capacity to cause pain. Mass is in kg (kilograms) and velocity is in meters/second. So the units of this pain, KE, are ` "kg" ("m"^2)/("s"^2) ` .
More Pain
Okay, let's suppose this time, instead of throwing the object at your head, I'm holding it over your head and I plan to drop it (I'm really turning out to be a mean S.O.B. aren't I). Now, what matters to you?
What else causes pain? Well, I could slap you...but that would probably be against the law. Besides, it's the same as the first case: how fast is my hand moving (squared) times how massive my hand is.
It Burns!!!
Another thing that causes pain is when something is very hot. The connection to the other cases might not be so obvious. But, let's suppose for a moment that the hot thing I'm touching is made of particles (I'll give you evidence for that soon) and temperature is related to how fast these particles are moving. Even in a solid, they are vibrating. The higher the temperature, the faster they are moving (some of you may already know that temperature is a measure of average Kinetic Energy). I can give you evidence to support this soon too, but it probably seems intuitive.
So, why does a thing at high temperature hurt? Because you are being hit by particles...yes, they are small, but there are a lot of them and they are moving very fast. In fact, the average velocity of molecules in air at room temperature is about 500m/s (about 1100 miles per hour). Temperature is a measure of the kinetic energy of the particles. So, again, we have the pain being related to ` "1/2mv"^2 ` and we have units of ` "kg" ( "m" ^2)/( "s" ^2) ` yet again.
Work, work, work:
So, we really have established the units of Energy, or, the capacity to cause pain. Okay most people talk about energy as capacity to do work. So, how should we define work? One type of work is when you lift or move something. Suppose you run out of gas and have to push your car. If you push on it, you are applying some force, so work must involve force. But, if you don't succeed in moving it, you haven't actually accomplished any work (in terms of moving the car, anyway). You have to move it some distance in order to do work. The farther you move it, the more work you have done. So, work is defined as force times distance–the amount of force you are applying, times the distance over which you apply it. You may remember from physics, F=ma (mass times acceleration), which means units of force are ` "kg" ( "m" )/( "s" ^2)` (we give this a special name, `1 "kg" ( "m" )/( "s" ^2) = 1 "Newton" `, or 1N). If I multiply that times the distance I move the object, I get ` "kg" ( "m" ^2)/( "s" ^2) ` , the same units we had above. So, these really are the units of energy. If that's the case, maybe we should give those units their own name, rather than having to write ` "kg" ( "m" ^2)/( "s" ^2) ` all the time. So, ` "1kg" ( "m" ^2)/( "s" ^2) = 1 "Joule" ` . Joule is abbreviated "J" and comes from the name of another famous dead guy, James Joule (you will become very familiar throughout the year with the “Famous Dead Guy” rule for naming units).
Let's make a law:
Or, let's make two. For now, we are going to do so without any theoretical underpinnings. We are just going to base it on observations.
A bowling ball at the top of a cliff has potential energy (PE=mgh). If I let it fall off the cliff, the potential energy decreases as the height drops. So, where does it go? Well, the ball moves faster, which means that its kinetic energy (KE=1/2mv2) is increasing. It turns out that the total increase in KE exactly matches the loss in PE. The reason I stressed "total" is that some of it goes to heat up particles in the air and the ball through friction. If the temperature of the air goes up, that's an increase in KE also. This fits with our law that energy is not created or destroyed, just converted between types of energy. Can you think of other examples?
Suppose that you have a tank of water and you stir it up and make some waves in it. You have just put energy into it, right? All the particles will be moving, so they will have Kinetic Energy (KE). Some will be in the tops (crests) of the waves. Particles in crest of a wave will be above the level of the water, so they will have gravitational PE, and will tend to fall back to the flat level. Over time, the water will calm back down and be flat on the surface.
What happened to the energy? Is it gone? Actually, no, all the energy will be in the form of KE uniformly distributed in the water, measured by its temperature. So, if our first law is right, the energy increase resulting in the gain in temperature (kinetic energy of the molecules) will be the same as the energy that you put into making the waves in the first place (James Joule, the famous dead guy for whom the unit of energy is named actually determined that the increase in temperature corresponded to the input kinetic energy). So, the energy is still there...it's just harder to recognize because it has become evenly distributed in the tank. That it tends to do that is our second law. It’s also worth noting that once the energy is evenly distributed, it is no longer very useful. You cannot do work with it.
The second law basically suggests that there is a "landscape" of energy analogous to the surface of the water, and it will tend to get flat and even over time. If there is one place that has more energy (kinetic or potential) than a spot next to it, the energy will tend to flatten out so that there are no peaks and valleys unless there is some barrier that keeps that from happening.
Think of some simple examples of this. Suppose you have a hot brick sitting in the middle of a room. Over time, the brick will cool down and the room will warm up. Eventually they will be the same temperature, which means all the particles will have the same average kinetic energy. There is no loss of energy here. At the start of the experiment, the particles in the brick had higher KE than those in the air in the room. They end up with uniform KE. Again, you go from energy concentrated in one location to energy evenly distributed.
Here's another one: suppose there is a ball sitting on the top platform of a ladder. It has potential energy. Even a modest nudge will push it off, and the ball will drop. When it settles on the ground, the potential energy is gone, converted to kinetic energy, eventually passing to kinetic energy of the particles the ball interacts with. The air particles and the molecules in the floor will each increase in kinetic energy (temperature). That is, the ball falling will convert the potential energy that resided entirely with the ball into kinetic energy dispersed among the particles in the air and floor (some of which is sound).
So, as was the case for the waves, high potential energy is an unstable state. Things at high PE will eventually fall to a state of lower PE because, when they do, they distribute the energy more evenly.
In the example of the ball, it only takes a small nudge to knock it off the ladder. Thus, chances are it will fall sometime. Now, if the ball were in a bucket glued to the top of the ladder, it would take more than a small nudge and it would not be as likely to fall. So, just because something could go to a lower potential energy, doesn't mean it will. The sides of the bucket represent a barrier to the energy distributing evenly.
Things in a high-energy state will tend to move to a lower energy state, so that energy will become more evenly distributed.
This is the big principle we have been working toward . This ultimately is why things happen.
Analogous to gravitational potential energy, there is a thing known as chemical potential energy. And the same things apply to it. Why does gasoline burn? Because when it does, the chemicals end up at a lower state of PE (like the ball falling) and pass the difference in energy onto the surroundings as heat (Some of it can be used to do work, like moving your car).
That’s another big theme: even though there is no net loss of energy, the transfer of energy can be used to do work. Once it is all evenly distributed, there’s nothing you can do with it.
Energy will tend to distribute evenly (entropy will increase). Because particles carry kinetic energy (unless they are at absolute zero), the distribution of particles will tend to become random over time because that distributes their energy. Why doesn’t everything fly apart into random distributions? Well, the universe as a whole seems to be heading that way. But, locally, things can stay fairly ordered-looking. Biological systems in particular seem very ordered.
It turns out there is another way to distribute energy more randomly: form bonds. You see, forming bonds always releases enthalpy, which can be loosely thought of as heat, to the surroundings. Conversely breaking bonds always requires input enthalpy.
This seems like forming bonds should be favored by our laws. If I release heat to the surroundings, I impart that energy to the surrounding particles, which can then distribute that energy more randomly.
But…there is a tension here.
Let’s consider the melting of ice or freezing of water. Most of you did a lab in the beginning of last year in which you saw that as water froze, heat was released to the surroundings. That’s consistent with what I just said: forming bonds releases enthalpy. That’s good because that released heat gets to distribute more randomly. But, forming bonds also restricts the motion of the molecules (in this case, water molecules become ice). That’s bad, because whatever kinetic energy the water molecules have gets pinned down in the crystal and can no longer distribute as widely.
On the other hand, when ice melts, the particles get to distribute more widely, carrying their energy and distributing it more randomly. That’s good. However, breaking the bonds of the ice crystal requires input enthalpy. That takes energy from the surroundings, cooling it down, and concentrates that energy as higher potential energy in the water molecules. That’s bad.
So, which one wins? Is it more energetically favorable for the bonds among the water molecules to form, releasing enthalpy to the surroundings, but constricting the molecules themselves? Or, does the freedom of the water molecules to move around win out? Does ice melt spontaneously or does water freeze spontaneously? The answer is, it depends on the temperature. And if you understand why, you understand a lot about energy.
At temperatures above 0oC (273K), pinning the molecules down is more costly. The higher the temperature, the more kinetic energy the molecules have, the more they are able to break the bonds holding the ice together, or, more correctly, the greater the benefit of letting them move freely. At temperatures below 0oC, however, the cost of taking enthalpy from the surroundings and using it to break the bonds is not offset by the benefit of releasing the molecules.
Notice while at really low or really high temperatures, you are likely to have all ice or all water. But, right at 0oC, you can have both ice and water. And, you can nudge it one way or the other by making relatively small changes to conditions. That’s because you are right at the point where the two players in the tug of war are equal to each other. This will be an important consideration in biology too.
We will come back again and again to breaking and reforming interactions. It is absolutely imperative for life that virtually all the reactions in our body be reversible, favoring one direction under some conditions and the other direction when those conditions change. We eke out a living at the margins of free-energy differences, always paying for it by heating up the surroundings (releasing enthalpy) satisfying the rule that we must increase the entropy of the universe.
By now you have heard “DNA contains the information that specifies living things.” Or perhaps you’ve heard it called a “blueprint.” You almost certainly have seen representations of it as a “double helix.” You may even have heard that “A” binds with “T” and “G” binds with “C.” (The four “bases,” are Adenine, Thymine, Guanine and Cytosine are abbreviated by their initial letters). But, how does DNA encode information? Why do “A” and “T” pair and not “A” and “C”?
Well, for one thing, adenine sometimes will bind with cytosine…just poorly and less stably. This is one way that mistakes, or mutations, happen when DNA is copied. The reason A binds with T most of the time and better than it would bind with C is simply because the change in energy is more favorable. The enthalpy released to the surroundings is greater when A binds with T than when A binds with C. It turns out that G binding with C releases even more energy.
The energy involved is very much along the same lines as that involved when ice freezes. In both cases, the bonds are hydrogen bonds, either among water molecules or between the bases of DNA.
If the analogy is to hold up, what do you think will happen to a pair of bases, A-T or G-C, if we raise the temperature? If the two strands are held together because of the same principles that hold water together as a liquid, or ice as a solid, what should happen to a double helix of DNA if I raise the temperature?
If you answered: “the bonds should break and the two strands of the helix should come apart,” you are correct. We even call this “melting,” the DNA.
This is just a first brush against a set of principles we will return to often in the coming weeks. The answer to questions like: “why do proteins fold up into their active shapes?”; “how does the muscle contract?” and many more will come down to the same simple principles, though applied in a rather complex pattern.
What is Energy?
This is trickier than it may seem, but it's very important that we have some understanding. One common definition is the capacity to do work. This begs the question: "what is 'work'?" Well, if you look that up, you find that work is a form of energy...that didn't help much.
I prefer to think of energy as "the capacity to cause pain." Yes, that's something of a joke, but it works better than you might think. Remember, the goal here is to come up with some way to relate things to each other. Pain is pain...we can all relate to it, no matter what causes it.
Imagine this: I'm standing before you with a spherical object I plan to throw at you; what are the things that matter to you? As the object is flying at your head, what determines how scared you are?
- how fast is it coming in at my head? (meters/second )
- how much does it weigh (or more properly, how much mass does it have, since it would hurt just as much if you were in space and the object were 'weightless'). Mass is in Kg.
The units of pain
It's worth thinking about the units for this measure of capacity to cause pain. Mass is in kg (kilograms) and velocity is in meters/second. So the units of this pain, KE, are ` "kg" ("m"^2)/("s"^2) ` .
More Pain
Okay, let's suppose this time, instead of throwing the object at your head, I'm holding it over your head and I plan to drop it (I'm really turning out to be a mean S.O.B. aren't I). Now, what matters to you?
- What is its mass? (kilograms, Kg)
- How high is it above your head? (meters, or "m")
- What planet are we on?
What else causes pain? Well, I could slap you...but that would probably be against the law. Besides, it's the same as the first case: how fast is my hand moving (squared) times how massive my hand is.
It Burns!!!
Another thing that causes pain is when something is very hot. The connection to the other cases might not be so obvious. But, let's suppose for a moment that the hot thing I'm touching is made of particles (I'll give you evidence for that soon) and temperature is related to how fast these particles are moving. Even in a solid, they are vibrating. The higher the temperature, the faster they are moving (some of you may already know that temperature is a measure of average Kinetic Energy). I can give you evidence to support this soon too, but it probably seems intuitive.
So, why does a thing at high temperature hurt? Because you are being hit by particles...yes, they are small, but there are a lot of them and they are moving very fast. In fact, the average velocity of molecules in air at room temperature is about 500m/s (about 1100 miles per hour). Temperature is a measure of the kinetic energy of the particles. So, again, we have the pain being related to ` "1/2mv"^2 ` and we have units of ` "kg" ( "m" ^2)/( "s" ^2) ` yet again.
Work, work, work:
So, we really have established the units of Energy, or, the capacity to cause pain. Okay most people talk about energy as capacity to do work. So, how should we define work? One type of work is when you lift or move something. Suppose you run out of gas and have to push your car. If you push on it, you are applying some force, so work must involve force. But, if you don't succeed in moving it, you haven't actually accomplished any work (in terms of moving the car, anyway). You have to move it some distance in order to do work. The farther you move it, the more work you have done. So, work is defined as force times distance–the amount of force you are applying, times the distance over which you apply it. You may remember from physics, F=ma (mass times acceleration), which means units of force are ` "kg" ( "m" )/( "s" ^2)` (we give this a special name, `1 "kg" ( "m" )/( "s" ^2) = 1 "Newton" `, or 1N). If I multiply that times the distance I move the object, I get ` "kg" ( "m" ^2)/( "s" ^2) ` , the same units we had above. So, these really are the units of energy. If that's the case, maybe we should give those units their own name, rather than having to write ` "kg" ( "m" ^2)/( "s" ^2) ` all the time. So, ` "1kg" ( "m" ^2)/( "s" ^2) = 1 "Joule" ` . Joule is abbreviated "J" and comes from the name of another famous dead guy, James Joule (you will become very familiar throughout the year with the “Famous Dead Guy” rule for naming units).
Let's make a law:
Or, let's make two. For now, we are going to do so without any theoretical underpinnings. We are just going to base it on observations.
- First, let's say that energy does not get created or destroyed in normal processes, just converted from one form to another. This law is called the first law of thermodynamics.
- Energy will tend to distribute evenly in the space available to it. This is one way to state the second law of thermodynamics. In it’s most general form, it says that a quantity called “the entropy of the universe” will always increase. Some books refer to entropy as a measure of disorder. But, that’s not really a good way to look at it. There is a very useful statistical definition of it I will save for later. For now, increased entropy means that the energy and mass have become more evenly and randomly distributed.
A bowling ball at the top of a cliff has potential energy (PE=mgh). If I let it fall off the cliff, the potential energy decreases as the height drops. So, where does it go? Well, the ball moves faster, which means that its kinetic energy (KE=1/2mv2) is increasing. It turns out that the total increase in KE exactly matches the loss in PE. The reason I stressed "total" is that some of it goes to heat up particles in the air and the ball through friction. If the temperature of the air goes up, that's an increase in KE also. This fits with our law that energy is not created or destroyed, just converted between types of energy. Can you think of other examples?
Suppose that you have a tank of water and you stir it up and make some waves in it. You have just put energy into it, right? All the particles will be moving, so they will have Kinetic Energy (KE). Some will be in the tops (crests) of the waves. Particles in crest of a wave will be above the level of the water, so they will have gravitational PE, and will tend to fall back to the flat level. Over time, the water will calm back down and be flat on the surface.
What happened to the energy? Is it gone? Actually, no, all the energy will be in the form of KE uniformly distributed in the water, measured by its temperature. So, if our first law is right, the energy increase resulting in the gain in temperature (kinetic energy of the molecules) will be the same as the energy that you put into making the waves in the first place (James Joule, the famous dead guy for whom the unit of energy is named actually determined that the increase in temperature corresponded to the input kinetic energy). So, the energy is still there...it's just harder to recognize because it has become evenly distributed in the tank. That it tends to do that is our second law. It’s also worth noting that once the energy is evenly distributed, it is no longer very useful. You cannot do work with it.
The second law basically suggests that there is a "landscape" of energy analogous to the surface of the water, and it will tend to get flat and even over time. If there is one place that has more energy (kinetic or potential) than a spot next to it, the energy will tend to flatten out so that there are no peaks and valleys unless there is some barrier that keeps that from happening.
Think of some simple examples of this. Suppose you have a hot brick sitting in the middle of a room. Over time, the brick will cool down and the room will warm up. Eventually they will be the same temperature, which means all the particles will have the same average kinetic energy. There is no loss of energy here. At the start of the experiment, the particles in the brick had higher KE than those in the air in the room. They end up with uniform KE. Again, you go from energy concentrated in one location to energy evenly distributed.
Here's another one: suppose there is a ball sitting on the top platform of a ladder. It has potential energy. Even a modest nudge will push it off, and the ball will drop. When it settles on the ground, the potential energy is gone, converted to kinetic energy, eventually passing to kinetic energy of the particles the ball interacts with. The air particles and the molecules in the floor will each increase in kinetic energy (temperature). That is, the ball falling will convert the potential energy that resided entirely with the ball into kinetic energy dispersed among the particles in the air and floor (some of which is sound).
So, as was the case for the waves, high potential energy is an unstable state. Things at high PE will eventually fall to a state of lower PE because, when they do, they distribute the energy more evenly.
In the example of the ball, it only takes a small nudge to knock it off the ladder. Thus, chances are it will fall sometime. Now, if the ball were in a bucket glued to the top of the ladder, it would take more than a small nudge and it would not be as likely to fall. So, just because something could go to a lower potential energy, doesn't mean it will. The sides of the bucket represent a barrier to the energy distributing evenly.
Things in a high-energy state will tend to move to a lower energy state, so that energy will become more evenly distributed.
This is the big principle we have been working toward . This ultimately is why things happen.
Analogous to gravitational potential energy, there is a thing known as chemical potential energy. And the same things apply to it. Why does gasoline burn? Because when it does, the chemicals end up at a lower state of PE (like the ball falling) and pass the difference in energy onto the surroundings as heat (Some of it can be used to do work, like moving your car).
That’s another big theme: even though there is no net loss of energy, the transfer of energy can be used to do work. Once it is all evenly distributed, there’s nothing you can do with it.
The Big Rule
Energy will tend to distribute evenly (entropy will increase). Because particles carry kinetic energy (unless they are at absolute zero), the distribution of particles will tend to become random over time because that distributes their energy. Why doesn’t everything fly apart into random distributions? Well, the universe as a whole seems to be heading that way. But, locally, things can stay fairly ordered-looking. Biological systems in particular seem very ordered.
It turns out there is another way to distribute energy more randomly: form bonds. You see, forming bonds always releases enthalpy, which can be loosely thought of as heat, to the surroundings. Conversely breaking bonds always requires input enthalpy.
This seems like forming bonds should be favored by our laws. If I release heat to the surroundings, I impart that energy to the surrounding particles, which can then distribute that energy more randomly.
But…there is a tension here.
Let’s consider the melting of ice or freezing of water. Most of you did a lab in the beginning of last year in which you saw that as water froze, heat was released to the surroundings. That’s consistent with what I just said: forming bonds releases enthalpy. That’s good because that released heat gets to distribute more randomly. But, forming bonds also restricts the motion of the molecules (in this case, water molecules become ice). That’s bad, because whatever kinetic energy the water molecules have gets pinned down in the crystal and can no longer distribute as widely.
On the other hand, when ice melts, the particles get to distribute more widely, carrying their energy and distributing it more randomly. That’s good. However, breaking the bonds of the ice crystal requires input enthalpy. That takes energy from the surroundings, cooling it down, and concentrates that energy as higher potential energy in the water molecules. That’s bad.
So, which one wins? Is it more energetically favorable for the bonds among the water molecules to form, releasing enthalpy to the surroundings, but constricting the molecules themselves? Or, does the freedom of the water molecules to move around win out? Does ice melt spontaneously or does water freeze spontaneously? The answer is, it depends on the temperature. And if you understand why, you understand a lot about energy.
At temperatures above 0oC (273K), pinning the molecules down is more costly. The higher the temperature, the more kinetic energy the molecules have, the more they are able to break the bonds holding the ice together, or, more correctly, the greater the benefit of letting them move freely. At temperatures below 0oC, however, the cost of taking enthalpy from the surroundings and using it to break the bonds is not offset by the benefit of releasing the molecules.
Notice while at really low or really high temperatures, you are likely to have all ice or all water. But, right at 0oC, you can have both ice and water. And, you can nudge it one way or the other by making relatively small changes to conditions. That’s because you are right at the point where the two players in the tug of war are equal to each other. This will be an important consideration in biology too.
We will come back again and again to breaking and reforming interactions. It is absolutely imperative for life that virtually all the reactions in our body be reversible, favoring one direction under some conditions and the other direction when those conditions change. We eke out a living at the margins of free-energy differences, always paying for it by heating up the surroundings (releasing enthalpy) satisfying the rule that we must increase the entropy of the universe.
A biological Example:
By now you have heard “DNA contains the information that specifies living things.” Or perhaps you’ve heard it called a “blueprint.” You almost certainly have seen representations of it as a “double helix.” You may even have heard that “A” binds with “T” and “G” binds with “C.” (The four “bases,” are Adenine, Thymine, Guanine and Cytosine are abbreviated by their initial letters). But, how does DNA encode information? Why do “A” and “T” pair and not “A” and “C”?
Well, for one thing, adenine sometimes will bind with cytosine…just poorly and less stably. This is one way that mistakes, or mutations, happen when DNA is copied. The reason A binds with T most of the time and better than it would bind with C is simply because the change in energy is more favorable. The enthalpy released to the surroundings is greater when A binds with T than when A binds with C. It turns out that G binding with C releases even more energy.
The energy involved is very much along the same lines as that involved when ice freezes. In both cases, the bonds are hydrogen bonds, either among water molecules or between the bases of DNA.
If the analogy is to hold up, what do you think will happen to a pair of bases, A-T or G-C, if we raise the temperature? If the two strands are held together because of the same principles that hold water together as a liquid, or ice as a solid, what should happen to a double helix of DNA if I raise the temperature?
If you answered: “the bonds should break and the two strands of the helix should come apart,” you are correct. We even call this “melting,” the DNA.
This is just a first brush against a set of principles we will return to often in the coming weeks. The answer to questions like: “why do proteins fold up into their active shapes?”; “how does the muscle contract?” and many more will come down to the same simple principles, though applied in a rather complex pattern.
