A-level Chemistry/AQA/Module 5/Thermodynamics/Energy, Work, Heat and the First Law

Internal Energy and the meaning of Temperature
The Internal Energy $$U$$ of a system is the sum of the energy of all it components and of all it interactions. Our components can be atoms or molecules. So, we know that the total energy of a system is composed by it Kinetic Energy $$K$$ (the energy of it components) and the Potential Energy $$V$$ (the energy of the interactions), so
 * $$U=\sum_{i=1}^NK_i+\sum_{i>j}V_{ij}$$

where $$N$$ is the amount of atoms or molecules of the system. We can have a system formed by molecules that rotate. The rotational energy must be included in the calculation of $$K$$. In this composite systems we may need skills to compute the value of $$U$$ for an arbitrary molecular systems, but it isn't the goal of Thermodynamics, but Statistical Mechanics. Here we can reveal the true nature of Temperature: we can say that is a measure of the Kinetic Energy of the system.

Ideal Gas
An Ideal Gas is a gas where there's no interaction between the molecules, so $$U=K$$

Cooling the system
We know that $$K>0$$ always, so $$T>0$$ always. This sentence is meaningless said this way, but it means that the system can't be cooled infinitely because there will be a moment where there's no Kinetic Energy to be lowered. We can set therefore a zero of the Temperature at $$K=0$$. So, Temperature it's an absolute magnitude.

Heat
The action on the system that make it raise the Internal Energy of the molecules without acting a force on them (that would be an interaction) is called Heat ($$Q$$). It doesn't matter if later the molecules act forces between them.

Work
The action on the system that make it raise the Internal Energy of the molecules only acting a force on them is called Work ($$W$$). Work is of the type of the force enacted (it can be mechanical work, electromagnetic, etc. ...)

First Law of Thermodynamics
Now we will set a equilibrium for the Internal Energy. The raise of $$U$$ is by Heat or Work, by definition, so
 * $$\Delta U= W+Q \,$$

Here there are many things to say. First, we have to say that $$U$$ is a quantity of the system that depends only of the time when it is measured; observables of this type will be called State Functions. $$\Delta U$$ is the difference of the Internal Energy of a system at the end of a process and at the beginning of it. Heat and Work, instead, are not state functions. This means that they depends on the process itself. So Energy doesn't depend of the process? Yes it does, but multiple processes that change Internal Energy in the same amount can have totally different Heats and Works.

Another thing to be said is that in the formula used below, $$W$$ and $$Q$$ are acted on the system, not by it. When they are acted by the system, are acted on the exterior of it, so is energy that the system lose, not gain; then we have to put the sign - on these terms when are acted by the system.

Now we have to understand how this apply to our surroundings, but that's another story.