Volume 25, Issue 1

Finite-time thermodynamics looks for the way of bringing a thermodynamic system from an initial to a final state, in a finite time. Usually a functional is extremized, e.g. the total entropy creation during the process is minimized. By means of simple electric circuits (with lumped resistors and lumped capacitors), we demonstrate that different assumptions can lead to quite different results.

The method of the entropy variation in thermodynamics, closely related to the mean-field Landau description and to the theory of Landau, is presented. it allows the formulation of a simple phenomenological approach for the metastable states, which allows one to calculate the explicit dependence of the Gibbs free energy on temperature, to calculate the heat capacity, the thermodynamic barrier, dividing metastable and more stable states, and the thermal expansion coefficient. Thermodynamic stability under mechanical loading is considered. The influence of the heating (cooling) rate on the measured dynamic heat capacity is investigated. A phase shift of the temperature oscillations of an ac heated sample is shown to be determined by the time of the relaxation of the metastable nonequilibrium state back to the metastable equilibrium one. This dependence allows one to calculate the relaxation time. A general description of the metastable phase equilibrium is proposed. Metastable states in AB 3 alloys are considered. Reasons for the change from the diffusional mechanism of the supercritical nucleus growth to the martensitic one as the heating rate increases are discussed. The Ostwald's stage rule is derived.

In this paper we build up, in a complete way, an Extended Thermodynamic theory of a nonviscous fluid in the presence of heat flux. The theory chooses as fundamental fields the density, the velocity, the energy density and the heat flux. The relations which constrain the constitutive quantities are deduced from the entropy principle, using the Liu method of Lagrange multipliers. These relations are exact, because no approximation has been used for their determination, and maintain their validity also for processes far from equilibrium. In the paper it is shown that the constitutive theory is determined by the choice of only four scalar functions of the intrinsic Lagrange multipliers. The complete nonequilibrium expressions of the chemical potential and of the entropy flux are determined: in these equations additional nonlinear terms appear, which are proportional to the Lagrange multiplier of a vector field related to the heat flux. The theory developed furnishes a nonlinear monofluid model of liquid helium II, in an inertial frame, in the complete absence of viscous phenomena. Nonlinear field equations for liquid helium II are written, a nonlinear boundary condition is formulated, two vector fields, which can be regarded as the velocities of the normal and the superfluid components of the two fluid model, are introduced.

Discrete kinetic theory approach has been used to study dilute, monatomic, non-equilibrium gas flow between two walls in microdomains. A four-velocity coplanar model has been adopted, where the microscopic velocity-orientation angle and the Knudsen number are free parameters, which have to be prescribed. Diffusive reflection boundary condition has been incorporated to obtain the solution. A bounded range for the admissible orientation angle of the discrete velocity vectors for any given Knudsen number is identified. Consequently, the macroscopic velocity slip at the wall, the velocity profile across the walls and the volume flow rate is calculated as a function of the free parameters. The calculations based on a single model, 4-velocity, cover the transition flow regime between the continuum and the free-molecular flow. The calculated volume flow rate is compared with experimental data as well as with other theoretical models.

Different dynamics of the non-equilibrium canonical density operator, such as Canonical Dynamics, Linear Projection Dynamics, Generalized Robertson Dynamics, and Contact Time Dynamics, especially for time dependent work variables are derived. For two discrete systems in contact the rate of entropy is non-negative, if the contact time is short, and if one of the two discrete systems is in equilibrium and the compound system composed of both is isolated. The contact temperature is identified with one of the Lagrange parameters of the non-equilibrium canonical density operator of the compound system.

The metabolic rates Г o = a o M 0.73 [W], a 0 = 3.6, of animals of different body masses M [kg] determines their heat production Q′ and their mechanical power output P . The metabolic heat production of small warm blooded animals living in a cold environment sets lower size limits for the body mass of birds and terrestrial mammals of M t,b ≥ 0.01 kg and M aq ≥ 10 kg for fast aquatic mammals. Birds must travel at the speed υ fl = 15 M 1/6 [m/s] in order to stay aloft, but their muscles only generate the metabolic velocity υ Г ≤≈ 50 M −0.25 [m/s]. These conditions yield an upper body size limit for flying birds: M b ,max ≤ 15 kg. Walking speeds scale with body mass as υ walk ∝ M 1/6 , while propagation speeds for endurance running are nearly independent of body mass. This makes walking faster than endurance running for animals with body masses M ≥ 600 kg.