# Thermodynamic definition of volume

• pigna
In summary, the textbook authors discuss the definition of a system, and explain that a system is defined by the presence of costituents, the external forces acting on the system, and the internal forces between the costituents. The state of a system is determined by the addition of two properties, energy and entropy.
pigna
I'm studynig thermodymamics using the textbook 'Thermodynamics foundations and applications' (Beretta and Gyftopopulos).
The definition of a system according to the authors consist in the specification of :

-the costituents of the system ( atoms or molecules or prottons neutrons ... in according to the scale of interest, or particles considering a continuum approach)
-internal and external force acting on the system; internal force are forces between the costituents of the system, while external forces are forces between the sistem costituents ad the costituents of the external environment, now if the system has to be
described in a determinsic way the external forces can't be functin of the positions of the costituents of the external environment and one has to find some parameters referred tho the system and his costituents able to model the effects of external forces.

For a large class of systems at equilibrium the patameters used to model the external forces can be reduced to volume so a system is defined as (V,n) where V is volum and n is the vector fo costituents. The state of the system is defined with the adding of a certain numbers of indipendent propreties; at Equilibrium are enougth 2 properties normally energy and entropy; it lead to the fundamental relation of the system:

U=U(S,V,n) or S=S(U,V,n)

where also V and n are properties of the system( it means that they can be found by a proper mesure procedure ), my problem rise here becasue in the book it
is not described the mesure procedure to find out volume, and it is not clear to me how volume is defined for a system. It is clear, thinking of the classical box filled with gas at equilibrium, that the volume of the system is not the sum of the volumes of the costituents.
So maybe volume is the achievable volume (the space the costituensts can occupy in according to their actual state), but these leads to a problem, because a property to be a property has to be measured in a certain istant of time, so if one wait to see where costituents are allow to move he mesure something that is not a property.
And what if the system in the box is not at equilibribrium or box doen't exist.

-If we consider the gas in a box in a non equilibrium state where the gas is tempotarily in a certain region of the box the volume of the system (the costituents of the sistem are the the gas molecules, the internal forces can be modeled or neglected, while the external forces are rapresented by the box) is the volume of the box or is a smaller one?
I suppose it is a smaller one.

-And also if we consider a close dinamical system (a system on which no external forces act), the fundamental equation at Equilibrium doesn't want the volume as a variable and became U=U(S,n) or S=S(U,n), but the volume can anyway be defined and maybe the fundamental relation can be written as U=U(V,n). in this case there is not a box and one has to find a definition of volume whithout the box. In this situation maybe exists a difference between systems dominated by gravitational forces and systems dominated by coulombian forces where could exists an excape velocity (i mean what is the volume of a collection of molecules close to each other and a molecule that has been escaped
and is moving whith his own velocity trough the empty space, has here volume a meaning ?)

I have read on callen the definition of volume from the the analisis of the normal modes of a system, but it is briefily explained and I'm still confused. All the stuffs I have read consider volume as a primitive macroscopic quantity and so they don't resolve my boubts.
If someone can suggest me a book or an article to make order in my mind i will be gratefull.

pigna said:
I have read on callen the definition of volume from the the analisis of the normal modes of a system, but it is briefily explained and I'm still confused. All the stuffs I have read consider volume as a primitive macroscopic quantity and so they don't resolve my boubts.
If someone can suggest me a book or an article to make order in my mind i will be gratefull.

if you visit the initial formulation of thermodynamics by Sadi Carnot -a french physicist- the attempt was as to how to derive work from a thermal system say 'steam' which was called working substance ;
the space occupied by the 'working substance ' was taken as volume and the surrounding as the environment - primitive definition can be a space surrounded by walls - the wall can have properties that it may be semipermeable to heat energy exchanges or it may be ideally adiabatic... the details you can see on wiki ref.<https://en.wikipedia.org/wiki/Thermodynamic_system>

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## What is the thermodynamic definition of volume?

The thermodynamic definition of volume is the amount of space occupied by a substance at a given temperature and pressure. It is a measure of the physical size of a system.

## How is volume related to temperature and pressure?

Volume is directly related to temperature and pressure according to the ideal gas law, which states that at constant pressure, the volume of an ideal gas is directly proportional to its absolute temperature.

## What are the units of volume in the thermodynamic definition?

The units of volume in the thermodynamic definition are typically cubic meters (m3) or liters (L). In some cases, other units such as cubic feet (ft3) or gallons (gal) may be used.

## How does volume change during a phase change?

During a phase change, such as from a solid to a liquid, the volume of a substance typically increases. This is because the particles gain more energy and move farther apart, taking up more space.

## What is the difference between specific and molar volume?

Specific volume is the volume per unit mass of a substance, while molar volume is the volume per mole of a substance. Molar volume is often used in thermodynamic calculations, while specific volume is more useful for engineering and practical applications.

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