Revised Interpretation of Work Potential in Thermophysical Processes

An alternative development is attempted of the concept of exergy or availability by introducing the idea that exergy represents an abstract thermodynamic metric that, essentially, quantie es the distance from the state of equilibrium with respect to a given reference value. Traditional and textbook approaches usually develop exergy asasystem’ spotentialtodoreversiblework.Usually,combiningthebalanceofenergyandentropyequationsmakes it possible to construct a corresponding balance of exergy and to use its dee nition to interpret the resulting terms. In contrast, the essential elements presented deal with the mathematical property of concavity of the entropy as the essence of the second law and how this property translates into a geometric complementarity relation between entropy and exergy. The balance of exergy equation is presented as an expression representing the corresponding convexity of the exergy, again demonstrating a mathematical property intrinsic to the second law. Nomenclature E = total energy density e = total specie c energy g = gravitational acceleration constant H = enthalpy density h = specie c enthalpy I = e ux or current of quantity k = coefe cient of thermal conductivity M = molecular mass m = mass P = thermodynamic pressure = thermal energy transfer rate (heating) R = gas constant S = entropy density s = specie c entropy T = temperature t = time U = internal energy density u = specie c internal energy V = volume = e uid velocity v = specie c volume = mechanical energy transfer rate (working) X = exergy density (also known as availability ) xk = Cartesian coordinates z = elevation level in a gravitational e eld b = thermal expansion coefe cient c = ratio of specie c heats D = total change in quantity d ij = Kronecker delta j = isothermal compressibility k = second coefe cient of viscosity l = e rst coefe cient of viscosity n = generic variable q = mass density s ij = viscous stress tensor u = specie c exergy w = specie c e ow exergy