Definition of the Moist-Air Exergy Norm: A Comparison with Existing “Moist Energy Norms”

This study presents a new formulation for the norms and scalar products used in tangent linear or adjoint models to determine forecast errors and sensitivity to observations and to calculate singular vectors. The new norm is derived from the concept of moist-air available enthalpy, which is one of the availability functions referred to as exergy in general thermodynamics. It is shown that the sum of the kinetic energy and the moist-air available enthalpy can be used to define a new moist-air squared norm that is quadratic in 1) wind components, 2) temperature, 3) surface pressure, and 4) water vapor content. Preliminary numerical applications are performed to show that the new weighting factors for temperature and water vapor are significantly different from those used in observation impact studies, and are in better agreement with observed analysis increments. These numerical applications confirm that the weighting factors for water vapor and temperature exhibit a large increase with height (by several orders of magnitude) and a minimum in the midtroposphere, respectively.

Role of thermodynamics in extensions of mesoscopic dynamical theories

Complex macroscopic systems (like for instance those encountered in nanotechnology and biology) need to be investigated in a family of mesoscopic theories involving varying amount of details. In this paper we formulate a general thermodynamics providing a universal framework for such multiscale viewpoint of mesoscopic dynamics. We then discuss its role in making extensions (i.e. in lifting a mesoscopic theory to a more microscopic level that involves more details).

THE LAWS OF THERMODYNAMICS AND THERMODYNAMIC STABILITY OF THE MODIFIED CHAPLYGIN GAS

Laws of thermodynamics have been examined for the universe filled with a perfect fluid, obeying an adiabatic equation of state p = γρ-A/ρα (called modified Chaplygin gas), where γ, A and α are positive constants and ρ and p are energy density and thermodynamic pressure respectively. Using general thermodynamics, the behavior of temperature and the thermodynamic stability has been discussed for modified Chaplygin gas. A scenario is obtained such that the thermal equation of state depends on both temperature and volume and there will be thermodynamic stability during the expansion process so that the fluid cools down through the expansion without any phase transition (or passing through any critical point).

THERMODYNAMIC STABILITY OF A FLUID WITH VARIABLE EQUATION OF STATE

This paper deals with general thermodynamics for the universe filled with a perfect fluid, obeying an equation of state p = ω(z)ρ where the varying equation of the state parameter is chosen as two-index parametrization models namely: (a) linear redshift parametrization: ω(z) = ω0 + ω1z or (b) Jassal–Bagla–Padmanabhan (JBP) parametrization: [Formula: see text] where ω0, ω1 are constants. The behavior of temperature and the thermodynamic stability have been discussed. The thermal equation of state depends on both temperature and volume. As the universe evolves the fluid cools down obeying third law of thermodynamics and there will be thermodynamic stability during the expansion process without any phase transition or passing through any critical point.