Infinite-step compression

Infinite-Step Compression. Notice that in compressing the gas isothermally, as the number of steps increases, the work required to compress the gas decreases. 

We summarize the results of these expansion and compression experiments in Table 10.3. The most important conclusion that can be drawn from these results can be stated as follows Only when the expansion and compression are both done reversibly (by an infinite number of steps) is the universe the same after the cyclic process (the expansion and the subsequent compression of the gas back to its original state). That is, only for the reversible processes is the heat absorbed during expansion exactly equal to the heat released during compression. In all the processes carried out using a finite number of steps, more heat is released into the surroundings than is absorbed in the comparable expansion (same number of steps). 

To overcome this computational dilemma, Constans et al. created an efficient algorithm that proceeds in different steps. Using the ASA method, the authors succeed in replacing the true integral measure of Eq. [21] by a summation, which was accomplished by introducing a function in the ASA density expression that effectively compresses the atomic shells. In the limit, the atomic electron densities are infinitely compacted into the nuclei. To illustrate the procedure, consider first expression [42]. A compression parameter 1 is introduced in the different shells such that... 

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