Lecture_21 - Lecture 21 Multistep processes w/o phase...

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Lecture 21 — Multistep processes w/o phase change. Haile analyzes an example process, that of compressing and heating CO 2 from 25C and 1bar, to 500C and 10bar. He considers four di ff erent processes to carry out the required state change. (sketch) You can read his lecture to see the details of how to calculate the heat and work required to carry out each process. The methods to calculate the heat and work are not new, except for the “irreversible adiabatic” process D, which I will discuss below. Here, I will comment on some aspects of the processes and results. First, note the convenience of plotting log P versus log v ; on such a log-log plot, isotherms of an ideal gas are straight lines with slope -1. Adiabats are likewise straight lines with slope - γ > 1. We cannot, however, view the area under the curve as equal to the work done in a reversible process, though we can compare such areas and tell if one process involves more work than another. Of the di ff erent paths Haile proposes, some are good for getting from state 1 to state 2 with the minimum mechanical work; some are good for getting there with the least heat added; some are good for getting there with the least heat removed. Depending on the “cost function” assigned to heating, cooling, and mechanical work, one path or another will be the most cost-e ff ective. To find the “best” path under some cost function is a problem in optimization. But we can get some insight into how di ff erent paths behave, by graphical reasoning. The “elements” of the di ff erent processes are familiar: Isothermal compression or expansion Adiabatic compression or expansion Heating or cooling at constant volume (isometric) Heating or cooling at constant pressure (isobaric) Sudden jump up or down in pressure (irreversible) Representing the process on a PV diagram is good for computing work e ff ects, but must integrate the specific heat (at constant volume, or pressure, as convenient) to get the heat.
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