- = Some gas is confined within a cylindrical container. The area of the base remains constant, but the height of the co

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Some Gas Is Confined Within A Cylindrical Container The Area Of The Base Remains Constant But The Height Of The Co 1 (136.15 KiB) Viewed 29 times

- = Some gas is confined within a cylindrical container. The area of the base remains constant, but the height of the container changes in time (think of a piston moving in a cylinder). Let's take the height to increase linearly with time: H(t) = Ho + at with a being constant. The initial gas density is uniform in space and given by po. Assume the velocity vector field to be one-dimensional, given by v(z, t) = kaz/H(t). (That is, v, increases linearly from zero at 0, to a at H(t).) Find the gas density as a function of time by solving the differential form of the continuity equation (conservation of mass), assuming the density to remain uniform in space and only varying with time. Is that solution consistent with the intuitive idea that the mass density is inversely proportional to the volume of the gas if the total mass is constant? z= =