Independent variables in termodynamics

[daudaudaudau]

Say I want to parametrize the plane. I can use cartesian (x,y) or polar (r,theta). But I cannot use x and r, because if I draw a circle and a vertical line, there are two points of intersection. I guess x and theta will do, because theta specifies a ray that will intersect any vertical line. Except when theta=pi/2 :-)

In thermodynamics we have a lot of variables and maybe three dimensions (for the ideal gas) connected through the equation of state. How can I know which combinations can parametrize the space and which can't ?

 

[LightHero]

The answer to this question will depend on the specific equation of state being used. Generally, it is possible to use any combination of variables that satisfy the equation of state for a given system. However, some combinations may be more useful than others, depending on the physical situation being studied. For example, if the system is in equilibrium, then it is often useful to choose variables such as pressure and temperature, which are intensive properties that do not depend on the size or shape of the system. If the system is out of equilibrium, then other variables such as composition or flow rate may be more appropriate. Ultimately, it is up to the researcher to decide which variables best describe the system under study.

 

[astrokreng]

In thermodynamics, the independent variables typically include temperature, pressure, and volume. These variables are used to describe the state of a system and are connected through the equation of state. Other variables, such as entropy and internal energy, can also be considered independent variables in certain thermodynamic processes.

When it comes to parametrizing a system, it is important to consider the relationships between the variables and how they affect the system. In the example given, using x and r to parametrize the plane may not be suitable because there are two points of intersection between a circle and a vertical line. This highlights the importance of choosing appropriate variables that accurately represent the system.

In thermodynamics, the choice of independent variables is often dictated by the specific system being studied. For example, in the ideal gas law, the independent variables are temperature, pressure, and volume. However, in different systems, different combinations of variables may be needed to fully describe the system.

To determine which combinations of variables can parametrize a system, it is important to understand the underlying principles and equations governing the system. In the case of thermodynamics, knowledge of the equation of state and the relationships between variables can help determine which combinations are suitable for parametrization.

In summary, the choice of independent variables in thermodynamics is dependent on the system being studied and the underlying principles governing the system. It is important to carefully consider the relationships between variables and choose appropriate combinations for parametrization in order to accurately describe and analyze the system.