Reversible adiabatic expansion of an ideal gas requires infinitely slow processes
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Retrieved reference literature and encyclopedic thermodynamic definitions establish that reversible adiabatic and quasi-static processes involving ideal gases require infinitesimally slow or gradual changes.
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Work performed by a Classical-"reversible"-Carnot cycle: Raising's distribution for the small "driving weights"
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The expansions or the compressions of the ideal gas in the quasi-static Carnot cycle, can be performed (on adiabatic or isothermal way) by slowly increasing or decreasing the external pressure by means of small weights acting on the piston of the vessel containing the gas. We call them shortly the ``driving weights'' (dw). Let N be their number, a large one.
To determine the work performed by the ideal gas in the cycle the ``driving weights'' must be handled carefully. If we let them move on-off the piston only horizontally, their vertical motions will be due only to the gas. Here we show that, at the end, while some of them will have moved down (will have negative raising) the remaining ones (the majority) will have moved up (will have positive raising) so that the total work performed by the ideal gas equals the total variation of the gravitational potential energy of the ``driving weghts''.
The cycle is performed in 2N time-steps. For each step t_i, with i in 1,..,2N, we give H(t_i), and DH(t_{i-1},t_i), respectively the height and the raising of the piston. Moreover the overall raising of the individual dw's (i.e. h_k, with k in 1...N), and their distribution are given in simple, general cases. The efficiency and the dissipated work are also evaluated.
This paper is aimed at imparting a deeper understanding of the ideal Carnot Engine and may also be useful as a segment in a didactic path on elementary calculus and statistics.
using the ideal gas law, or the hydrostatic equation for atmospheric processes. In practice, no process is truly adiabatic. Many processes rely on a large
An adiabatic process (adiabatic from Ancient Greek ἀδιάβατος (adiábatos) 'impassable') is a type of thermodynamic process that occurs without transferring heat between the thermodynamic system and its environment. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work and/or mass flow. As a key concept in thermodynamics, the adiabatic process supports
If the system has such rigid walls that work cannot be transferred in or out (W = 0), and the walls are not adiabatic and energy is added in the form of heat (Q > 0), and there is no phase change, then the temperature of the system will rise.
If the system has such rigid walls that pressure–volume work cannot be done, but the walls are adiabatic (Q = 0), and energy is added as isochoric (constant volume) work in the form of friction or the stirring of a viscous fluid within the system (W < 0), and there is no phase change, then the temperature of the system will rise.
If the system walls are adiabatic (Q = 0) but not rigid (W ≠ 0), and, in a fictive idealized process, energy is added to the system in the form of frictionless, non-viscous pressure–volume work (W < 0), and there is no phase change, then the temperature of the system will rise. Such a process is called an isentropic process and is said to be "reversible". Ideally, if the process were reversed the energy could be recovered entirely as work done by the system. If the system contains a compressible gas and is reduced in volume, the uncertainty of the position of the gas is reduced, and seemingly would reduce the entropy of the system, but the temperature of the system will rise as the process is isentropic (ΔS = 0). Should the work be added in such a way that friction or viscous forces are operating within the system, then the process is not isentropic, and if there is no phase change, then the temperature of the system will rise, the process is said to be "irreversible", and the work added to the system is not entirely recoverable in the form of work.
If the walls of a system are not adiabatic, and energy is transferred in as heat, entropy is transferred into the system with the heat. Such a process is neither adiabatic nor isentropic, having Q > 0, and ΔS > 0 according to the second law of thermodynamics.
Naturally occurring adiabatic processes are irreversible (entropy is produced).
The transfer of energy as work into an adiabatically isolated system can be imagined as being of two idealized extreme kinds. In one such kind, no entropy is produced within the system (no friction, viscous…
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Work performed by a Classical-"reversible"-Carnot cycle: Raising's distribution for the small "driving weights"peer-reviewedno side taken