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Let = (,) be the internal energy (heat) per unit volume of the bar at each point and time. The rate of change in heat per unit volume in the material, ∂ Q / ∂ t {\displaystyle \partial Q/\partial t} , is proportional to the rate of change of its temperature, ∂ u / ∂ t {\displaystyle \partial u/\partial t} .
The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable, a thermodynamic potential, and an extensive property. [5] Thermodynamics defines internal energy macroscopically, for the body as a whole.
This is due to the way that metals bond chemically: metallic bonds (as opposed to covalent or ionic bonds) have free-moving electrons that transfer thermal energy rapidly through the metal. The electron fluid of a conductive metallic solid conducts most of the heat flux through the solid. Phonon flux is still present but carries less of the energy.
Solidity ≡ The ratio of the volume of solid to the bulk volume, or the ratio of bulk density to solid grain density, d B /d G. Robertson, p. 5. Beryllium oxide: 218 [37]-260 [47]-300 [47] TPRC Recommended 424 302 272 196 146 111 87 70 57 47 39 33 28.3 24.5 21.5 19.5 18.0 16.7 15.6 15.0 List [32] 293 [47] 200 273.2 300 400 500 600 700 800 900 ...
Carnot was aware that heat could be produced by friction and by percussion, as forms of dissipation of "motive power". [8] As late as 1847, Lord Kelvin believed in the caloric theory of heat, being unaware of Carnot's notes. In 1840, Germain Hess stated a conservation law for the heat of reaction during chemical transformations. [9]
The internal energy of a body can change in a process in which chemical potential energy is converted into non-chemical energy. In such a process, the thermodynamic system can change its internal energy by doing work on its surroundings, or by gaining or losing energy as heat.
Just as with the internal energy version of the fundamental equation, the chain rule can be used on the above equations to find k+2 equations of state with respect to the particular potential. If Φ is a thermodynamic potential, then the fundamental equation may be expressed as:
The flow of heat from Earth's interior to the surface is estimated at 47±2 terawatts (TW) [1] and comes from two main sources in roughly equal amounts: the radiogenic heat produced by the radioactive decay of isotopes in the mantle and crust, and the primordial heat left over from the formation of Earth. [2]