By Kleppner .D And Kolenkow R.
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Extra info for An introduction to mechanics Solutions Manual
The internal energy associated with the bonds in a molecule is called the chemical or bond energy. There is an enormous amount of internal energy associated with the bonds within the nucleus of the atom itself. This energy is called nuclear energy and it is released during nuclear reactions. A property is any characteristic associated with a system. Properties are usually classiﬁed as intensive and extensive. Intensive properties are those which are independent of the size of a system. Extensive properties are those whose values depend on the size or extent of the system.
Usually g˙ th is taken as +ve for heat source and −ve for heat sink. Therefore, for conservation of energy, ρ (δxδyδz) c ∂T = ∂t . 4) that is, ρc ∂T = ∂t . 5) is the general form of the heat diﬀusion equation. This equation, usually known as the heat equation, provides the basic tool for heat conduction analysis. Solving the heat equation, we can obtain the temperature distribution T (x, y, z) as a function of time. The thermal conductivity k being a material property depends on the temperature and other physical properties of the material.
Recognizing that the heat ﬂux is a vector quantity, we can write a more general statement of the heat conduction rate equation (Fourier’s law) in the following form. 2) ✐ ✐ ✐ ✐ ✐ ✐ “K13693” — 2012/1/31 — 9:52 ✐ ✐ Introduction 25 where the Laplacian (or del) is the three-dimensional operator, ∂ ∂ ∂ +j +k ∂x ∂y ∂z ≡i and T (x, y, z) is the scalar temperature ﬁeld. 2) is the diﬀerential form of the Fourier’s law of heat conduction. It implies that, the heat ﬂux is in the direction perpendicular to the isothermal surfaces.