Non equilibrium thermodynamics: T as a function of time

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Discussion Overview

The discussion revolves around the calculation of average temperature as a function of time in a non-equilibrium thermodynamic system consisting of two gases brought together without barriers. Participants explore the complexities of temperature and pressure distribution during the transient state.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification

Main Points Raised

  • One participant inquires about an equation to calculate the average temperature in a combined gas system over time, highlighting the initial inhomogeneity of temperature and pressure.
  • Another participant suggests that simulating the system using the Navier–Stokes equations could be a viable approach, indicating that analytic equations may provide reasonable approximations for certain conditions.
  • A further contribution emphasizes the necessity of including the differential energy balance equation to account for heat conduction within the system.
  • The original poster expresses gratitude and acknowledges the complexity of the problem, indicating a recognition of the challenges involved.

Areas of Agreement / Disagreement

Participants do not reach a consensus on a specific equation or method, and multiple approaches are suggested without resolution on which is preferable.

Contextual Notes

The discussion does not clarify specific assumptions or limitations regarding the systems' properties or the conditions under which the proposed equations would be valid.

pterodox
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Hi.
Let's say we have two separate systems (containing gases), each with their own temperature, pressure and volume. Then these systems are brought together, with no walls in between. Of course, one might consider they are now technically the same system, but the distribution of pressure and temperature is inhomogeneous for a while.
Is there an equation that I could use to calculate the average temperature of any volume inside this space as a function of time?
Thanks.
 
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You can simulate the system, sure. The Navier–Stokes equations are probably a good start.
Analytic equations might give reasonable approximations for some setups.
 
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In addition to what mfb said, you would also have to include the differential energy balance equation to include heat conduction within the system.
 
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Thank you both! I'll look into those. This might be a bit tougher than I initially expected.
 

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