We start off this chapter talking about energy, heat, and work in terms of a system and all the shit that's around it...the surroundings. A system can be isolated, closed, or open.
An isolated system can't exchange anything with it's surroundings...not energy and not matter. I equate this to forming a bacterial lawn on an agar plate and letting the thing grow, but not taking anything away (waste products) and not adding anything (like extra nutrients) while the bacterial colony undergoes whatever processes it undergoes.
A closed system can exchange energy but not matter with the surroundings...That's basically our planet.
We don't really exchange much with outer space short of sending out the occasional astronaut or satellite
A system can also be open, exchanging both energy and matter with the surroundings.
A system's internal energy is basically all the energy that it exchanges by means of physical processes and chemical reactions. This includes whatever it's atoms/molecules do, the energy stored in bonds (that can then be broken/reformed), and the energy of non-covalent interactions (the crap that I talked about earlier....charge-charge, charge-dipole, etc). Those are all associated with a certain amount of energy.
A system's internal energy depends on the thermodynamic state.
The thermodynamic state is defined by asking questions like...how much and what kind of crap is in your system? You also use 2/3 variables to define it, including temperature, pressure, and volume.
Only isolated systems cannot exchange energy with the surroundings. Exchanging energy means changing it's internal energy, thereby giving us ΔU
When a system is closed (like earth), exchange of energy and thereby change in internal energy occurs by either transfer of heat or work done. The work includes either the system doing work on the surroundings or the surroundings doing work on the system. When you exert a force against a resistance, you are doing work.
When we take the energy that can be exchanged in a closed system, separate it into heat and work, you get positive and negative values of both.
When you have +q, the system is absorbing heat from the surroundings. -q means the system is releasing heat into the surroundings.
Likewise, when you have +w, work is being done by the system on the surroundings and when we have -w, work is being done by the surroundings, on the system.
Bringing this into more of a real thing perspective, when we eat crap, we're ingesting glucose. That gets oxidized to carbon dioxide and water, which has an energy change associated with that particular process. The energy released, we can use in the form of heat or work. It's kind of neat.
All of this ties into the First Law of Thermodynamics.
In a closed system (like the earth), internal changes in energy occur via heat or work that is exchanged with the surroundings.
So we get that formula, for overall change in internal energy, dependent on heat and work done.
If we consider a system that absorbs heat at the same rate that it does work on it's surroundings (where both q and w will be positive, and equal to each other), you'll have no overall change in internal energy because everything evens out.
Any change that could occur in internal energy is going to depend on the initial and final states of the system and is going to be "path independent" meaning if there are two ways to accomplish something, that is irrelevant and the only thing we care about is the change in energy. But the amounts of heat and work individually that are released/absorbed by the system are going to depend on what happens between the initial and final states....that shit is path dependent. This way, we get into this picture that I'm not going to draw, there is no way in hell, so I'll just take a photo of the book:
The book takes these two experiments that are basically doing the same thing...oxidizing one mol of palmitic acid. The reaction is basically
1 mol acid + 23 mol Oxygen --> 16 mol CO2 + 16 mol H20
The book talks about running this reaction in two ways, and then figuring out which of the ways is more alike to what happens when the reaction occurs in our body.
First, the reaction is run at constant volume, which is definitely not our body state, because if that were the case, we would explode.
This is done using a bomb calorimeter. So you've got some palmitic acid with some oxygen and you ignite the sucker in a sealed up box that's inside of a water bath, which has a thermometer to gauge the temperature difference in the water.
When you ignite the insides, you measure the heat that goes from the system (closed up bomb container) to the surroundings (the water with the thermometer that's measuring this). Since this shit is constant volume, no work is being done to/by the surroundings...so in our
Δ U = q-w
Δ U = q - 0
Δ U = q
The total change in internal energy that's going on here is just the heat that goes from the bomb thing to the water bath around it....At constant volume, the internal energy change that is going on is the heat that is released from the system to the surroundings.
Heat is measured in joules and the value of ΔU here is going to be -9941.4 kj/mol of palmitic acid.
The value is negative because the reaction is releasing energy that's stored in bonds. As heat in this situation went from the bomb thing (system) to the water bath (surroundings), the energy in the system decreased.
If you do this same reaction at constant pressure instead of constant volume, you get something different going on.
In this case, when you ignite the bomb thing, instead of being constrained by volume, there's this piston thing that move up and down. The bomb thing (I'm just going to call it bomb thing) is free to expand and contract because of the piston thing when you ignite the sucker. So you ignite it, the reaction happens, the piston moves up, then down, and finally we have it contract in proportion to how many moles of gas we LOST. Remember, we started with 23 mol of oxygen and we get only 16 mol of CO2 in our products. Since we now have less gas volume, this means that work was done by the surroundings on the system.
So in this constant pressure system, we can use some formulas and shit to get to a good way to calculate the work that is being done.
Work is done when volume is changed against pressure, and using PV=nRT, where R is the gas constant, T the absolute temp (K), and n is the number of moles changing, we get all that crap above.
And here is the actual calculation of the value of work, in J/mol of crap, which you can then convert to kj/mol of crap in the next photo...
Uhhhh so this is kind of important. You're figuring out some stuff here which differentiates the two scenarios.
You're kind of moving the formula ΔU = q-w ....since you already have the ΔU (from the constant volume experiment) and you have the w which we calculated from the previous part, we can get the q value by adding the change in internal energy to the work that was done in this constant pressure thing.
What this means is that under constant-pressure systems, we get some more heat released to the surroundings than in constant volume. In the constant pressure version, the surroundings are able to do work on the system, and you can measure this work as the extra heat that gets released from the system.
This is where all the path independence/dependence crap comes from. Heat and work that are varying in systems depend on path but the internal energy doesn't.
In the next post, we'll talk about the places where I get most confused...enthalpy and entropy. Entropy not so much, but I still get sad with enthalpy because I feel like I understand it wrong.
No comments:
Post a Comment