[Thermodynamics] Macrostates - Volume, Moles, Pressure, Temperature

[imdow123]

I'm trying to understand thermodynamics in a more concrete and precise way and I'm planning to start by defining all the macrostates.

One thing we do in thermodynamics is instead of calculating for every atom its momentum, energy etc. we define some microstates that are observable and measurable, right?

 

So what all macrostates do we define? I tried to come up with macrostates without referring anywhere and here is the list:-

1) Volume - How much space the matter is occupying

2) Moles - How much matter is there in the volume

3) Pressure - How fast the matter is moving

 

These are the only states I could come up. It seems as if all other states are derived from this. Temperature, entropy, energy in my opinion can be derived from these three. Am I right?

 

EDIT: Mistake in title, should be macrostate instead of microstate

Edited October 3, 2013 by imatfaal
fixed that title for you - imatfaal

[studiot]

 

Am I right?

 

 

In a word no. Classical thermodynamics is much more complicated than that.

 

Suppose I told you that I had 1 mole of substance A in a container, open to the air at the top, of 1 litre volume.

 

What can you tell me about its thermodynamics?

 

Can you identify substance A, or even tell me what state it is in?

Edited October 2, 2013 by studiot

[imdow123]

I don't know if state has a different meaning in Thermodynamics but here I'm using it as a measurable physical quantity of the whole system.

So you say that volume, pressure and moles are not enough to describe thermodynamics of a substance? Why is that? What else can you observe about a substance?

Also an additional question - Why can't temperature be derived from volume, pressure and moles. For me volume, pressure and moles describe the whole dynamics of the system. There is space occupied (volume), amount of matter(moles) and how matter is behaving(pressure) all three things so intuitively it is enough. Where am I going wrong?

Does my question even make sense?

[studiot]

I expect you are thinking only of gases?

 

There are many other states of matter, called phases in thermodynamics.

 

How would you derive the phase rule from your quantities?

 

And how did you get on with my questions in post#2?

 

Classical thermodynamics is much more complicated than that.

 

I am having some difficulty understanding where you are coming from. Have you , for instance, done a course in statistical thermodynamics ?

 

Perhaps if you asked for some explanation, rather than made sweeping generalisations someone could help more.

 

Thermodynamics is a wonderful subject, and worth a deal of effort.

[imdow123]

I have done a course in statistical thermodynamics. Now I'm trying to understand it in a better way.

 

As for your question in post #2 :-

That's what I'm asking. Why isn't volume, moles and pressure enough to describe the dynamics of some system? Can you why we need more macrostates no describe the system?

[imdow123]

As my question seems unclear I would like to rephrase it and make it clearer.

I will also tell what I understand by specific terms, please correct me if I'm wrong.

 

Thermodynamics to me is about defining some states that are observable and measurable instead of calculating motion of individual atoms which would be quite cumbersome.

[i'm worried only about gases at the moment] So the standard way we start with thermodynamics is define things like pressure, volume, number of moles and temperature. A simple equation governs these states given by PV = nRT.

 

What I'm now asking is that why do we need four states i.e. pressure, volume, moles and temperature.

Why can't we do it with three things i.e. volume (amount of space that gas is occupying), moles (amount of matter in the system) and pressure (how the matter is moving). For me, these three things seem to be enough intuitively.

 

Thank You!

[studiot]

Since you are online at the moment, I started an overview, but have not finished it yet.

 

Here is the beginning, let me know if you would like me to carry on.

 

Here is an overview of thermodynamics and the relationship between statistical and classical thermo.

 

Thermodynamics divides the universe into two parts by a specified boundary.

 

The part of interest is called the system and the rest of the universe is called the surroundings. Any particular thermo problem can be made easier or more difficult or even impossible by appropriate choice of boundary i.e. what we choose to include or exclude in our system.

 

Properties of interest are defined by variables. Variables are called extensive if they are proportional to the amount (mass) of matter present and intensive if they are independent of mass. Some variables are neither extensive nor intensive.

 

Some variables are directly observable (measurable), some have to be deduced from various available relationships that exist between variables.

 

Conditions within a system may be static or most often they are changing. This presents two immediate difficulties.

 

Firstly for intensive variables we have one value to represent the whole system, however unless the system is homogenous and isotropic the value varies from point to point within the system especially as changes occur. Examples are temperature and pressure, two important directly observable properties.

 

Note with extensive properties no such difficulty exists since we can take the value over an (infinitesimally) small region and sum to obtain the value for the whole system. It does not matter whether there is local variation from point to point the answer is still the same. So we can add up all the mass points or heat capacities of a system to find the overall value.

 

I will return to the second difficulty after discussion of the boundary.

 

Whilst classical thermo, in conjunction with kinetic theory, offers some relationships between some of the variables within a system, for example the gas laws, it mostly concentrates on exchanges across the boundary.

 

So the First Law is concerned with energy that crosses the boundary in the form of work, heat, change of phase etc.

 

Statistical thermo, on the other hand, is not so much concerned with the source or flows of this energy, but with its distribution and redistribution within a system. Boltzman’s Law being its crowning glory.

 

Energy flow across the boundary is another example of directly measurable quantities.

 

In order to know about the system we define a condition known as a ‘state’. We can do this if we can allocate values to ‘variables of state’. These include Pressure, Volume, Temperature, and a number of derived (calculated ) variables such as internal energy, entropy and so on.

 

Variables of state are such that the change in the value of a variable of state from one state to another equals the difference in its value in each state.

 

Work and heat flow (cross boundary variables) are not variables of state.

 

You can immediately see that this leads to the second difficulty. If for instance the pressure in a gas is not homogenous you do not have a single value to insert for pressure in relations relating pressure to another quantity. The same goes for temperature.

The non linear nature of most of the formulae mean that averages are unsuitable substitutes.

 

So classical thermo has devised several prongs of attack on this difficulty.

 

Firstly for an infinitesimal change we can regard all properties as unchanged. So if we can find and integral formula and integrate it we can still calculate.

 

Secondly the idea of the cyclic process. If we return the system to its starting point we can find formulae for the net effects in terms of the cycle. Much classical theory takes place in terms of cyclic processes. These are unnecessary in statistical thermo.

 

Thirdly we can sometimes find alternative expressions for a quantity. For instance the work done across the system boundary. It is obvious that the work done by the system must equal the work received by the surroundings. So although we cannot directly calculate the work done expanding most gaseous systems, because we do not know the pressure at all times at all points, if the expansion is against say the atmosphere we can say this is sensibly constant and calculate the work this way.

 

 

In order to properly specify and analyse a thermodynamic system we must specify

 

The system components

The system boundary

The system process

.

Edited October 3, 2013 by studiot

[imdow123]

Thanks for your effort. Please carry on.

 

Observable variables are I suppose volume, pressure and moles.

Please shed some light on temperature too. Is it a deduced relationship from existing variables? Why / why not?

[studiot]

I have extended the discussion in post#7

 

Please ask questions, I'm sure there will be some.

[imdow123]

Everything is clear except this. I should've come to the point earlier.

 

Why do we need temperature as a variable of state? Can't temperature be derived from Pressure, Volume and number of moles?

I understood everything else. Just clear my concept of temperature.

[studiot]

Without the temperature variable, how would you solve the following problem with all the information given, except the temperature rise?

 

That is you are given the number of moles, the pressures and volumes exactly as in the problem.

 

http://www.scienceforums.net/topic/79099-thermodynamics-example-with-answer/

 

This is the simple practical answer.

 

 

 

We can discuss a more esoteric one if you like.

 

The Zeroth Law of Thermodynamics requires the existence of a temperature state function. This can be proved using the Gibb's Formulation of thermodynamcis in terms of generalised co-ordinates.

Edited October 4, 2013 by studiot

[imdow123]

I just realised my doubt more clearly. Can't temperature be derived from pressure, volume and moles? If yes, then the problem can be solved.

[Bignose]

I just realised my doubt more clearly. Can't temperature be derived from pressure, volume and moles? If yes, then the problem can be solved.

The answer is, it depends.

 

Pressure is a function of the number of collisions a gas makes with a surface. I.e. the pressure on a cylinder is directly the number of collisions the gas molecules make with the cylinder and the speed at which to collisions occur.

 

In an ideal gas, pressure and temperature can be directly calculated from one another. This can be seen easily from the Ideal Gas Law, PV=nRT, especially since the constraints of the question above are that you also know moles (n) and volume (V).

 

But, it isn't as straight forward for non-ideal gases. If the molecules interact at all, the way the molecules collide with one another and surfaces (i.e. that cylinder wall again) aren't are straightforward. Just having the pressure -- again a measure of how many collisions and how speedy they are -- isn't enough to know the temperature. You have to know how the molecules interact with walls & each other. i.e. square well potential? Leonard-Jones potential? and so on.

 

Whether you can treat a gas as ideal or not really depends on the necessary accuracy of the question being asked, and the conditions you are trying to calculate about.

[studiot]

 

I just realised my doubt more clearly. Can't temperature be derived from pressure, volume and moles? If yes, then the problem can be solved.

 

 

I'm sorry, how was this a response to my post#11?

 

I have stated specifically that what you ask is not possible, so why repeat?

 

I need to know whether you have heard of the Zeroth Law or Gibbs Formulation or generalised coordinates to discuss this.

[imdow123]

Basically temperature is a measure of direction of flow of heat from one body to other. So according to this definition it should depend on physical properties of the bodies and not be a basic state itself. That is why, I asked if it is a fundamental state or a derived state.

[studiot]

 

Basically temperature is a measure of direction of flow of heat from one body to other. So according to this definition it should depend on physical properties of the bodies and not be a basic state itself. That is why, I asked if it is a fundamental state or a derived state.

 

 

You have posed a very deep question, but your attempt at answer is insufficient.

 

Thermodynamics is much more complicated than that, and I thought you wanted to go on to deeper things.

 

That is why I have been trying to find the level to pitch a suitable answer.

 

For an single phase as a single component ideal gas in equilibrium only Temperature can be derived from a PV diagram.

That is because for this system every point on the diagram corresponds to a unique state and thus a unique calculation according to the ideal gas law can be made.

 

Now if the system is not in equilibrium it cannot be plotted on a PV diagram.

 

Further if you have a PV diagram for water there are points on the diagram that will not return a unique temperature, even when the water is in an equilibrium state.