Parameters of State in the Global Thermodynamics of Binary Ideal Gas Mixtures in a Stationary Heat Flow

• Published in: Entropy (Basel, Switzerland) Vol. 25; no. 11; p. 1505
• Main Authors: Maciołek, Anna, Hołyst, Robert, Makuch, Karol, Giżyński, Konrad, Żuk, Paweł J.
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.11.2023
• Subjects: Binary mixtures; Concentration gradient; Degrees of freedom; Energy; Energy trading; Entropy; entropy and internal energy; Equilibrium; Flow mapping; Gas mixtures; Gases; Heat; Heat flux; Heat generation; Heat transfer; Heat transmission; Ideal gas; Internal energy; Mathematical analysis; mixtures and parameters of state; non-equilibrium thermodynamics; Parameters; Steady state; Temperature; Thermodynamic equilibrium; Thermodynamics
• ISSN: 1099-4300; 1099-4300
• DOI: 10.3390/e25111505

In this paper, we formulate the first law of global thermodynamics for stationary states of the binary ideal gas mixture subjected to heat flow. We map the non-uniform system onto the uniform one and show that the internal energy U(S*,V,N1,N2,f1*,f2*) is the function of the following parameters of state: a non-equilibrium entropy S*, volume V, number of particles of the first component, N1, number of particles of the second component N2 and the renormalized degrees of freedom. The parameters f1*,f2*, N1,N2 satisfy the relation (N1/(N1+N2))f1*/f1+(N2/(N1+N2))f2*/f2=1 (f1 and f2 are the degrees of freedom for each component respectively). Thus, only 5 parameters of state describe the non-equilibrium state of the binary mixture in the heat flow. We calculate the non-equilibrium entropy S* and new thermodynamic parameters of state f1*,f2* explicitly. The latter are responsible for heat generation due to the concentration gradients. The theory reduces to equilibrium thermodynamics, when the heat flux goes to zero. As in equilibrium thermodynamics, the steady-state fundamental equation also leads to the thermodynamic Maxwell relations for measurable steady-state properties.