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The law is frequently qualified to include the condition that the temperature difference is small and the nature of heat transfer mechanism remains the same. As such, it is equivalent to a statement that the heat transfer coefficient, which mediates between heat losses and temperature differences, is a constant.
The volume of phase space , occupied by a system of degrees of freedom is the product of the configuration volume and the momentum space volume. Since the energy is a quadratic form of the momenta for a non-relativistic system, the radius of momentum space will be so that the volume of a hypersphere will vary as giving a phase volume of
Laser action is also a non-equilibrium process, but it depends on departure from local thermodynamic equilibrium and is thus beyond the scope of classical irreversible thermodynamics; here a strong temperature difference is maintained between two molecular degrees of freedom (with molecular laser, vibrational and rotational molecular motion ...
The macroscopic energy equation for infinitesimal volume used in heat transfer analysis is [6] = +, ˙, where q is heat flux vector, −ρc p (∂T/∂t) is temporal change of internal energy (ρ is density, c p is specific heat capacity at constant pressure, T is temperature and t is time), and ˙ is the energy conversion to and from thermal ...
A property of a physical system, such as the entropy of a gas, that stays approximately constant when changes occur slowly is called an adiabatic invariant.By this it is meant that if a system is varied between two end points, as the time for the variation between the end points is increased to infinity, the variation of an adiabatic invariant between the two end points goes to zero.
The temperature-entropy conjugate pair is concerned with the transfer of energy, especially for a closed system. An isothermal process occurs at a constant temperature. An example would be a closed system immersed in and thermally connected with a large constant-temperature bath. Energy gained by the system, through work done on it, is lost to ...
where we have first used the definition of entropy in classical thermodynamics (alternatively, in statistical thermodynamics, the relation between entropy change, temperature and absorbed heat can be derived); and then the second law inequality from above. It therefore follows that any net work δw done by the sub-system must obey
In mathematics, if given an open subset U of R n and a subinterval I of R, one says that a function u : U × I → R is a solution of the heat equation if = + +, where (x 1, ..., x n, t) denotes a general point of the domain.