What are the Three Main Types of Connections in Thermodynamics?

[aaaa202]

It seems to me that for some thermodynamic variables it makes sense to talk of systems in contact with different values of these variables. An example is temperature. We can the problem of two systems in contact with different temperatures.
However, I am not sure if this is the case for all thermodynamic variables. Consider for instance the pressure. How would you treat a system of two gasses in contact with different pressures - for me it doesn't make sense.
What property of the temperature (which is not a property of pressure) makes us able to treat it as described above?
The question came to be because chemical potential was treated as temperature where you had two systems in contact with different chemical potentials. Is this allowed?

 

[Chestermiller]

It seems to me that for some thermodynamic variables it makes sense to talk of systems in contact with different values of these variables. An example is temperature. We can the problem of two systems in contact with different temperatures.
However, I am not sure if this is the case for all thermodynamic variables. Consider for instance the pressure. How would you treat a system of two gasses in contact with different pressures - for me it doesn't make sense.
What property of the temperature (which is not a property of pressure) makes us able to treat it as described above?
The question came to be because chemical potential was treated as temperature where you had two systems in contact with different chemical potentials. Is this allowed?

See my Blog in my PF personal area.

Chet

 

[Rap]

There are three main types of "connections" - thermal, mechanical, and material. A thermal connection allows entropy to flow, mechanical allows "volume to flow", and material allows mass to flow across the boundary. Thermal, mechanical, and material isolation prevent the flows. In other words, a thermal barrier prevents two bodies from exchanging entropy (heat cannot flow across the boundary due to a temperature difference), a mechanical barrier prevents them from exchanging volume (the barrier doesn't move when subjected to a pressure difference), and a material barrier prevents them from exchanging mass (particles are prevented from crossing the boundary when subjected to a chemical potential difference). When you talk about temperature differences equilibrating, you are assuming mechanical and material isolation. When you talk about a pressure difference, the boundary is a thermal barrier, and a material barrier, so what happens is the boundary moves, like a piston in a cylinder with different pressures on each side. If you want two or three of the boundary conditions to be conducting (i.e., not a barrier), then things can get more complicated.