Describing system in terms of 2 variables vs natural variables

In summary, the conversation discusses the use of partial derivatives to express a function's differential and how any system can be uniquely specified by two parameters. The concept of natural variables is also brought up, with pressure and temperature being the natural variables for Gibbs free energy. However, there are other thermodynamic potentials that have different natural variables. The conversation also mentions the topic of statistical physics and its relation to quantum field theories.
  • #1
I<3NickTesla
12
0
Realised I probably posted this in the wrong forum before, should've been here..

I often see a function's differential expressed in terms of convenient partial derivatives eg
dU=(dU/dT) dT + (dU/dV) dV

And I've seen it written that "any system is uniquely specified by two parameters, such as pressure and volume, or perhaps pressure and temperature"

But then what's the deal natural variables? What's so "natural"/good about them if any pair will do? By natural I mean that I've seen the natural variables for gibb's energy as pressure and temperature.
 
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  • #2
right, for the Gibbs free energy, the natural variables are pressure and temperature. But there are other thermodynamic potentials than just the Gibbs free energy, and they will have some other natural variables. http://en.wikipedia.org/wiki/Thermodynamic_potential
This website is pretty good. I'll admit that I don't know as much about statistical physics as I would like to know. It is a pretty interesting topic. And then it naturally leads to things like quantum field theories. (i.e. related to renormalisation and phase transitions and symmetry and stuff).
 

What is the difference between describing a system in terms of 2 variables and natural variables?

Describing a system in terms of 2 variables refers to using 2 independent variables to describe the behavior of a system, while natural variables are the most fundamental variables that describe a system without needing to specify any additional parameters.

Why is it important to use natural variables when describing a system?

Using natural variables allows for a more concise and accurate description of a system, as they are the most fundamental and intrinsic parameters of the system. They also help to eliminate any unnecessary parameters or assumptions.

What are some examples of natural variables?

Some examples of natural variables include temperature, pressure, and volume for a gas system, and mass and position for a simple pendulum system. These variables are independent of any specific units or measurement scales.

How do natural variables relate to the laws of thermodynamics?

The natural variables of a system are directly related to the laws of thermodynamics, as they are used to define the state of a system and determine its behavior. The first law of thermodynamics, for example, states that the change in internal energy of a system is equal to the heat added to the system minus the work done by the system, and this can be expressed in terms of natural variables.

Can a system be described using both 2 variables and natural variables?

Yes, a system can be described using both 2 variables and natural variables. However, using natural variables is generally preferred as it provides a more fundamental and accurate description of the system. The use of 2 variables may be necessary in certain situations, such as when studying a specific aspect of the system's behavior or when trying to simplify the analysis of a complex system.

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