State functions

[Toadie]

I realize that this is supposed to be a really easy concept, but I have a hard time understanding it.

 

Could someone please try to explain to me what a state function is, without saying "a quantity that depends only on the current equilibrium state of the system" or something essentially similar? Particularly I would much appreciate it if someone could show me some examples of how things like heat and work do depend on the way the system acquired the state?

 

 

Thanks a bunch

[insane_alien]

i'll reword it in a simpler way that you'll perhaps understand.

 

An equation of state is a function that describes the present state of a system in a single value that is independant of the history of the system.

 

basically it means, the history of the system is irrelevant, the current state doesn't depend on it.

 

this is true, it is impossible to determine whether a system has undergone a reaction or you have just mixed fresh reagents in the proportions likely to be found after a reaction is completed.

[hermanntrude]

I realize that this is supposed to be a really easy concept, but I have a hard time understanding it.

 

Could someone please try to explain to me what a state function is, without saying "a quantity that depends only on the current equilibrium state of the system" or something essentially similar? Particularly I would much appreciate it if someone could show me some examples of how things like heat and work do depend on the way the system acquired the state?

 

 

Thanks a bunch

 

many textbooks have a worked example of a system containing some gas which is compressed. The deltaH is calculated and the work done on the system is also calculated. First the compression is done in a single step and then it's done in two smaller steps, and the work turns out to be different for the two steps.

 

If you have a large library nearby, I know there's an example like that in "general chemistry: principles and applications" by petrucci, herring madura and someone else too, 9th edition. However, it's probably in lots of other books in one other form.

[timo]

An equation of state is a function that describes the present state of a system in a single value that is independent of the history of the system.

You can usually not describe the state of a system in a single value. The (macro-) state of an ideal gas can be described by the volume, the number of particles and the total kinetic energy, for example. None of these three parameters can be omitted.

[insane_alien]

yes, i know it doesn't fully describe the state of the system, but it ascribes a value to it that is a mathematical relationship of those various parameters and is immensly useful when the system is changing as it can be described by this changing value.

 

equations of state just provide useful values for detwermining the properties.

[timo]

I guessed so. It's just that your post could be interpreted as states being fully described by a single parameter. Btw: You seem to use the terms "state function" and "equation of state" interchangeably. Typically, the terms are not presented as being two different names for the same thing - but I don't really get the difference. To quote from Atkins:

Pg13: That is, it is an experimental fact that each substance [remark: The chapter is called "The properties of gases"] is described by an equation of state, an equation that interrelates these four variables [V, N, p, T].

 

Pg48: The internal energy is a state function in the sense that its value depends only on the current state of the system [...]. In other words, it is a function of the properties that determine the current state of the system.

 

Also, I think I only met the term "equation of state" in the context of the "caloric equation of state" and "thermal equation of state" (translations from German by me, maybe the terms do not even exist in English).

 

Perhaps the different terms is historic in that thermodynamics was first purely an emperical/experimental field ( -> equation of state ) and only later put on solid theory ( -> state functions ).

 

Concerning the original question:

Perhaps it is easier to understand what a state function is by trying to understand what is not a state function. Take a nuclear power plant. Assume you have some water in state L (liquid). Then, the water is vaporized. The vapor drives a turbine generating electrical energy. By doing so, it cools down. Then, maybe after some additional cooling, it is put back into the reservoir (I just assume there was a water reservoir in power plants - I'm not an engineer) and again is in state L. By looking at the water in the reservoir you cannot tell how much electrical energy was produced with this water. So the electrical energy produced is not a state function.

Or, as an even simpler although not typical thermodynamical example: I am at my computer now and I was there five hours ago. But that does not define how many kilometers I walked within these five hours -> The distance I traveled is not a state function of my position.