Ideal Gas Laws
In Part II, our description of fluid behavior differs from our description of the dynamics of masses and springs, strings, bars, and two-dimensional vibrating surfaces. In Part I, it was reasonable to identify the coordinates of a specific point on such a vibrating system and write an equation for the time evolution of that point based on Newton’s Second Law of Motion and some description of the appropriate elastic restoring force. With fluids, it is rare that we identify a “specific point” in the fluid and try to track the motion of that parcel of fluid. With fluidic systems (gases and liquids), we generally adopt a different perspective, since it is inconvenient (and frequently impossible) to identify a specific “fluid particle” and track its flow under the influences of various forces and boundaries. Instead, we choose to identify a differential volume, dV = dx dy dz, specified in coordinates (x, y, and z) that are fixed in our laboratory frame of reference, while calculating the changes in the properties of the fluid within that differential volume (e.g., pressure, density, temperature, enthalpy, fluid velocity, mixture concentration, void fraction, dielectric polarization) as we keep track of the amount of fluid that enters or leaves that (fixed in space) differential volume. The fact that we no longer choose to identify individual fluid parcels requires the introduction of a mass conservation equation (also known as the continuity equation), in addition to our dynamical equation (Newton’s Second Law) and our constitutive equation (Hooke’s Law or some other equation of state).
KeywordsHeat Capacity Sound Speed Isobaric Heat Capacity Viscous Stress Tensor Isochoric Heat Capacity
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