By C. Truesdell
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Additional info for Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Treated as a Branch of Rational Mechanics
McGraw-Hill, 1969. 14 I. 32) a, = a - a,n. In particular, the scalar quantity q1 is t h e j u x of energy out of the body. 33) In stating it we have not included a term to represent radiation or other local sources of heat, for no such possibility is allowed in the kinetic theory of MAXWELL. 4). While opinions differ as to what the Second Law of Thermodynamics ” is, the Clausius-Duhem inequality is the most commonly accepted mathematical statement of that law in the rather scant literature that comes to grips with dissipative processes in deformable continua of some generality.
10)l,2as postulates. The rate of dissipation vanishes if and only if tj = 0; that is, a flow of a linearly viscous fluid is dissipationless if and only fi it is isocaloric. 21) shows, the dissipation due to viscosity is the sum of two non-negative parts: one associated with bulk viscosity, and one associated with shear viscosity. In a fluid such that the shear viscosity or the bulk viscosity vanishes, the corresponding rate of dissipation of energy is null in all flows. 10)l,2are equivalent to the requirement that the mechanical part of the rate of dissipation of energy be non-negative in every flow.
38) itself, sometimes heat-transfer condition, asserts that at each point on dB called MAXWELL'S where 8 Ow, heat flows into 899 or out of 893 according as 8 < Ow or 8 > Ow. The statement that heat never Pows from the colder body to the hotter is sometimes regarded as implied by or being a part of the " Second Law ". 38) has a status, whether we choose to regard it as directly founded on experience or as a part of some sort of protophysics. + No inconsistency between the heat-bath inequality and the Clausius-Duhem inequality has been found here.
Fundamentals of Maxwell's Kinetic Theory of a Simple Monatomic Gas, Treated as a Branch of Rational Mechanics by C. Truesdell