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Motivating free energy (2013) (redirected from Motivating the Gibbs free energy (2013))

Page history last edited by Joe Redish 6 years, 1 month ago

Working Content > Thermodynamics and statistical physics

 

Prerequisites:

 

Biological systems are continually occupied with collecting, organizing, storing and utilizing energy.  Systems from cells to organs to organisms collect energy in various forms, control the flow of materials to and from compartments within cell, organs, and organisms, and maintain their temperatures to prevent harmful side effects such as the unraveling of proteins (denaturation) and the failure of cell membranes.  From a biology perspective, metabolic pathways provide a wonderfully complex roadmap to many of these processes and highlight how energy flows through a biological system. 

 

Here we consider the flow of energy from a physics perspective, and ask how the  foothold principles of physics and thermodynamics we already studied constrain how energy can flow in a biological system.  We will tackle the following questions:

 

  • Where is localized energy available?
  • What conditions will allow that localized energy to spontaneously transform?
  • How much of that energy can I use?

 

Consider a simple example: a box with gas on one side and vacuum on the other as shown in the figure below.

 

 

If we remove the dividing membrane and allow the molecules of the gas to move into double its original volume, the molecules will hardly notice it. Whatever kinetic energy they have originally they will still have. This tells us that their temperature will not change, but their density will drop by a factor of 2 so the pressure will drop by the same factor as the volume increases. (The molecules will collide with the walls less often.)

 

When the molecules were all on the left, we might have extracted some energy from the gas. For example, instead of simply removing the partition, we might have punctured a small hole in it and let the gas stream out from the left into the right. We could then have put a little wind turbine in the path of the stream of gas and let it turn the turbine charging a battery. When the gas is equally distributed, the fan would be hit by the same number of molecules from each side so it would stop turning, but we would have extracted some energy from the gas -- and the resulting temperature would be lower. The question we are interested in is, how much energy can we extract from the gas? All of it? Only some of it? We identify any energy that we can extract from system as free energy. To figure out how much this is we have to think about the constraints of the first and second laws of thermodynamics.

 

When we try to predict how a system will evolve -- that it, how its energy and concentrations will spontaneously rearrange themselves, the first and second law of thermodynamics prescribe two tendencies:

 

  • If any work is done by the system, we expect the system to move toward lower energy.
  • From considerations of what we know about statistics and probability, as expressed by the Second Law of Thermodynamics, we expect the system moves toward higher entropy.

 

"Free energy" is a way of combining both of these tendencies into a single quantity that tells you how a system will tend to evolve.  There are different free energies out there, which are appropriate in different situations (for example, in some physics contexts, it's useful to apply Helmholtz free energy), but the one useful in biology is Gibbs free energy (named after Josiah Willard Gibbs), since it's defined for a system at constant temperature and pressure, which describes the environment inside a cell.

 

 

But wait a second:  Doesn't the First Law (conservation of energy) tell us that energy always stays constant?  Yes, the energy of the whole universe stays constant, but, as described by the First Law, a system can gain or lose energy from/to its surroundings. Similarly, the Second Law tell us that entropy always increases for the whole universe, but not necessarily the entropy of a given system.  If a system loses entropy, its surrounding has to gain at least as much entropy so that the total entropy of the universe still increases (so the Second Law isn't violated).  

 

If the system is staying at constant temperature and pressure as it is interacting with its surroundings via heat and work, the Gibbs free energy helps us sort out what will happen to the energy of the system .  

 

Follow-ons:

 

 

 Workout

 

Ben Dreyfus and Joe Redish 2/3/12

Wolfgang Losert 2/5/2013

Class content > Thermodynamics and statistical physics

 

Prerequisites:

 

Biological system appear to continually occupied with the storage and flow of energy:  Cell, organism, and whole organisms always collect (mostly chemical) energy, control the flow of proteins, lipids and other small molecules to and from the surrounding medium, and maintain their temperatures.  Primary considerations for a biological system are the following:

 

  • Where is localized energy available?
  • How will that localized energy spontaneously transform?
  • How much of that energy can I use?

 

Consider a simple example: a box with gas on one side and vacuum on the other as shown in the figure below.

 

 

If we remove the dividing membrane and allow the molecules of the gas to move into double its original volume, the molecules will hardly notice it. Whatever kinetic energy they have originally they will still have. This tells us that their temperature will not change, but their density will drop by a factor of 2 so the pressure will drop by the same factor as the volume increases. (The molecules will collide with the walls less often.)

 

When the molecules were all on the left, we might have extracted some energy from the gas. For example, instead of simply removing the partition, we might have punctured a small hole in it and let the gas stream out from the left into the right. We could then have put a little wind turbine in the path of the stream of gas and let it turn the turbine charging a battery. When the gas is equally distributed, the fan would be hit by the same number of molecules from each side so it would stop turning, but we would have extracted some energy from the gas -- and the resulting temperature would be lower. The question we are interested in is, how much energy can we extract from the gas? All of it? Only some of it? We identify any energy that we can extract from system as free energy. To figure out how much this is we have to think about the constraints of the first and second laws of thermodynamics.

 

When we try to predict how a system will evolve -- that it, how its energy and concentrations will spontaneously rearrange themselves, we see two tendencies:

 

  • From considerations of what we know about chemical reactions, we expect the system to move toward lower (potential) energy -- more deeply bound states. If a reaction is exothermic, we expect it to tend to go in that direction.  Because of the way chemical bonding works (where bonded molecules are at lower potential energy), this tends to make things bond together.
  • From considerations of what we know about statistics and probability, as expressed by the Second Law of Thermodynamics, we expect the system moves toward higher entropy. This can have the opposite effect, tending to make things break apart (since if there are more pieces, there are more possible ways to arrange them).  This also tends to make things mix up (e.g. diffusion).

 

"Free energy" is a way of combining both of these tendencies into a single quantity that tells you which direction a system will tend to evolve.  There are different free energies out there, which are appropriate in different situations (for example, some physicists like Helmholtz free energy), but the one useful in biology is Gibbs free energy (named after Josiah Willard Gibbs), since it's defined for a system at constant temperature and pressure, which better describes the environment inside a cell.

 

But wait a second, why do we have to balance two different factors?  Doesn't the First Law (conservation of energy) tell us that energy always stays constant?  Yes, the energy of the whole universe stays constant, but, as described by the First Law, a system can gain or lose energy from/to its surroundings. Similarly, doesn't the Second Law tell us that entropy always increases, period?  Yes, the entropy of the whole universe always increases, but not necessarily the entropy of a given system.  If the system is staying at constant temperature and pressure, that means it is interacting with its surroundings, via heat and work.  (You've seen examples of this with work on the enthalpy page, and with heat in the temperature regulation activity.) These interactions can change the entropy of the surroundings.  So it's possible that the entropy of the system will decrease, but the entropy of the surroundings will increase by a greater amount, so that the total entropy of the universe still increases (so the Second Law isn't violated).  This doesn't always happen, but it can.  To know whether or not it happens in any given situation, we need Gibbs free energy to tell us.

 

Follow-ons:

 

Ben Dreyfus and Joe Redish 2/3/12

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