Can I rearrrange this work equation?

[Gerrard]

We all know this classic equation

Work=-pressure external*delta volume

and

Pressure*Volume=#molecules*R(constant)*Temperature

Can I rework the equation to be

Work=-pressure (external)*delta (#molecules*R(constant)*Temperature/Pressure)
 

[swansont]

There are a bunch of ways that you can rearrange the thermodynamic potentials equations, but you need to be careful. W = -P (delta V) assumes constant T and n 

You can't just pop it into an equation where T and/or n is not constant

[studiot]

Given the information Dr Swanson has given you the best possible answer, but it is very short. +1

A little more context would elicit a fuller and hopefully better answer.

[swansont]

Check out Gibbs and Helmholtz free energies, which relate to non-PV work. Note that they, too, make assumptions about variables being held constant.

https://socratic.org/questions/what-are-helmholtz-free-energy-and-gibbs-free-energy

[Gerrard]

Why does is assume n and T are constant.

 

For example, if you have a balloon with 10PSI at 25 C and a volume of 20L. If the temperature goes to 35 C, then you simply put in the changes into the equation right? The temperature of 35C and any potential pressure change to calculate work. 

[swansont]

29 minutes ago, Gerrard said:

Why does is assume n and T are constant.

 

For example, if you have a balloon with 10PSI at 25 C and a volume of 20L. If the temperature goes to 35 C, then you simply put in the changes into the equation right? The temperature of 35C and any potential pressure change to calculate work. 

You can’t solve PV = nRT without also knowing what happens to all the variables. T changes. Does V changes? Does n?

[Gerrard]

1 minute ago, swansont said:

You can’t solve PV = nRT without also knowing what happens to all the variables. T changes. Does V changes? Does n?

No n does not change in this situation. 

[swansont]

13 minutes ago, Gerrard said:

No n does not change in this situation. 

So why it an issue that I said n has to be constant?

The thing is, if you change one variable, the others can change, and where the energy goes depends on that. Temperature changes, for example, represent a change in energy that’s not available to do PV work. 

[joigus]

I concur with swansont. Only, I think he meant,

W = - delta(PV) assumes constant P

when he said,

On 4/18/2020 at 1:13 PM, swansont said:

W = -P (delta V) assumes constant T and n 

as W = -P(delta V) is just the definition of work for a P, V, T, n system (the simplest ones.) And when n, T are constant ==> d(PV)=0 ==> W = -pdV = +VdP (for that case in an ideal gas.)

Just to offer a mathematical perspective. If you differentiate (increment) PV=nRT, you get

PdV+VdP = nRdT

(d=your "delta"=increment, small change)

or for varying n,

PdV+VdP = RTdn+nRdT

because, as swansont says, you must know what's changing in your process, and how. You see, in thermodynamics you're always dealing with processes. To be more precise, reversible processes (That doesn't mean you can't do thermodynamic balances for irreversible processes too, which AAMOF you can.). Whenever you write "delta," think "process."  So, as swansont rightly points out, what's changing in that process?

The culprit of all this is the fact that physics always forces you to consider energy, but in thermodynamics, a big part of that energy is getting hidden in your system internally, no matter what you do, in a non-usable way. This is very strongly reflected in the first principle of thermodynamics, which says that the typical ways of exchange of energy for a thermal system (work and heat) cannot themselves be written as the exchange of anything even though, together, they do add up to the exchange of something (here and in what follows, "anything," "something," meaning variables of the thermodynamic state of a system: P, V, T, PV, log(PV/RT), etc.) 

So your work is -PdV, but you can never express it as d(something). We say it's a non-exact differential.

It's a small thing, but not a small change of anything

The other half of the "hidden stuff" problem is heat, which is written as TdS, S being the entropy and T the absolute temperature, but you can never express it as d(something). Again, a non-exact differential. And again,

A small thing, but not a small change of anything

Enthalpy and Gibbs free energy are clever ways to express heat exchange and work as exact differentials, under given constrictions for the thermodynamic variables.

And Helmholtz's free energy is something like the mother of all thermodynamic potentials and its true pride and joy.

Edited May 5, 2020 by joigus
mistyped

[MigL]

In much simpler terms...

P, V, and T are independent variables, and can be considered just like x, y, and z coordinates in math.
You can have a function which tells you how V changes with T on the V-T plane, where P is a fixed value ( held constant ).
You can have a function which tells you how P changes with T on the P-T plane, where V is a fixed value ( held constant ).
You can have a function which tells you how V changes with P on the V-P plane, where T is a fixed value ( held constant ).
Edit: forgot to mention n can also be an independent variable.

Or, once  you get to higher math, you can have a partial differential equation which describes the 'surfaces' in P-V-T space relating the three variables.
See here...              http://mutuslab.cs.uwindsor.ca/schurko/introphyschem/handouts/mathsht.pdf 

Edited May 5, 2020 by MigL

[studiot]

4 hours ago, MigL said:

P, V, and T are independent variables, and can be considered just like x, y, and z coordinates in math.

I have to disagree with this.

The OP implies that the system is not open by omitting n in the original statement. So mass is constant.

So P, V and T are not all independent since they are connected by an equation of state.
Only two of them are.

The point of x,y,z, coordinates is that they are independent unless you are restricting the subject to some part of x,y,z space.

7 hours ago, joigus said:

The culprit of all this is the fact that physics always forces you to consider energy

That's a bold statement which merits some strong justification.  What about the distinction between dynamics and kinetics?

AFIK there is no mention of energy in kinetics.

[joigus]

6 hours ago, MigL said:

P, V, and T are independent variables, and can be considered just like x, y, and z coordinates in math.

 

1 hour ago, studiot said:

I have to disagree with this.

 

1 hour ago, studiot said:

So P, V and T are not all independent since they are connected by an equation of state.
Only two of them are.

I have to agree with studiot's disagreement. That's one of the most common obfuscations when studying thermodynamics (TD). In TD you never go outside the surface of state, defined by the equation of state f(P,V,T,n)=0. That's why they most emphatically are not independent variables. This is commonly expressed as the fundamental constraint among the derivatives:

which leads to unending "circular" pain when trying to prove constraints among thermodynamic coefficients of a homogeneous substance, for teachers and students alike.

 

1 hour ago, studiot said:

That's a bold statement which merits some strong justification.  What about the distinction between dynamics and kinetics?

AFIK there is no mention of energy in kinetics.

'Kinetics' is kind of a loaded word. Do you mean dynamics vs kinematics in the study of motion, or as in 'kinetic theory of gases', 'chemical kinetics'?

Sorry, I really don't understand. But I would really be surprised that a theory about anything in Nature missed the energy arguments. Sometimes you can do without it, but there are very deep reasons for energy to be of central importance. I would elaborate a bit more if you helped me with this.

Edited May 5, 2020 by joigus

[studiot]

14 minutes ago, joigus said:

1 hour ago, studiot said:

That's a bold statement which merits some strong justification.  What about the distinction between dynamics and kinetics?

AFIK there is no mention of energy in kinetics.

'Kinetics' is kind of a loaded word. Do you mean dynamics vs kinematics in the study of motion, or as in 'kinetic theory of gases', 'chemical kinetics'?

Sorry, I really don't understand. But I would really be surprised that a theory about anything in Nature missed the energy arguments. Sometimes you can do without it, but there are very deep reasons for energy to be of central importance. I would elaborate a bit more if you helped me with this.

No one is disputing the fundamental nature of energy considerations.
Or that these can save a considerable amount of effort compared to other methods and routes to a solution of a particular problem.
Virtual work springs immediately to mind.

But it is not the only game in town.

Indeed I think you would be hard pushed to find an energy consideration in the equations/conditions of compatibility for a subject area, for example the continuity equation which I suggest is equally fundamental.
But  then energy consideraions are usually classified under the equations of constitution.

Nothing loaded about the word kinetics. Yes it was the first thing that sprang to mind when I mentioned it and I was referring to kinematics, which specifically excludes the causes (force, energy, action etc) of the motions. However I am not sure how energy is involved in the geometry of a random walk in 'the kinetic theory' or and it is not often involved in chemical kinetics, or the calculation of p values, say pH for instance.

You may have heard of this delightful book by Mark Levi

The Mathematical Mechanic.

https://books.google.co.uk/books/about/The_Mathematical_Mechanic.html?id=lW5vQK6Tcu8C&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false

Mark has some very interesting ideas about using energy methods.

 

[joigus]

1 hour ago, studiot said:

No one is disputing the fundamental nature of energy considerations.
[...]

But it is not the only game in town.

I totally agree. In fact, in the topics of physics that are dearest to my heart, it is my conviction that we must overcome this concept.

1 hour ago, studiot said:

Nothing loaded about the word kinetics. Yes it was the first thing that sprang to mind when I mentioned it and I was referring to kinematics, which specifically excludes the causes (force, energy, action etc) of the motions. However I am not sure how energy is involved in the geometry of a random walk in 'the kinetic theory' or and it is not often involved in chemical kinetics, or the calculation of p values, say pH for instance.

I see your point. I went back to my sentence and I think what I meant (or must have, or should have meant) is "The culprit of all this is the fact that thermodynamics always forces you to consider energy."

Instead of,

10 hours ago, joigus said:

The culprit of all this is the fact that physics always forces you to consider energy,

 

1 hour ago, studiot said:

You may have heard of this delightful book by Mark Levi

The Mathematical Mechanic.

https://books.google.co.uk/books/about/The_Mathematical_Mechanic.html?id=lW5vQK6Tcu8C&printsec=frontcover&source=kp_read_button&redir_esc=y#v=onepage&q&f=false

Mark has some very interesting ideas about using energy methods.

No, I haven't, but from perusing the first pages --although the energy arguments weren't there--, it looks like a very interesting outlook. It reminds me of what Perelman did to solve the Poincaré conjecture: consider the Ricci flow to prove a topological statement. That's using a physical idea to solve a mathematical problem.

I would talk more about this delightful topic, but my kinetics is forcing me to slow down. Maybe later.

It's been a pleasure.

[studiot]

2 minutes ago, joigus said:

It's been a pleasure.

Thanks and nice to have a sensible converstaion. +1

[MigL]

On further reflection, I have to agree with your disagreements.
( it was midnight, what can I say )