Systems and State Point Information

Equations of state convert input variables to output. The latter anticipate properties of a system that can be checked by experiment. The infrastructure of Sections 3.1 and 3.2 is famously applicable to systems and input-output conversions. The proviso is that the conditions conform to equilibrium—the most probable states are manifest, there is zero available work, and so forth. 

Let the ideal gas equation be used to convert experimentally measured V, n, and T into output let the result be 5774 pascals. Upon the fourth measurement, the chemist finds the pressure dial to read 5654 pascals—the ideal gas equation overestimated by 120 pascals. Then if p is measured subsequent times, the results should equate with the ideal number minus a correction of 120 pascals. If the van der Waals equation is used instead to anticipate p, a similar situation arises. The correction should be smaller as account has been taken of the nonideality. 

The preceding is not 100% accurate because it implies that repeated measurements afford zero information. It implies that the probability of observing p = 5654 

Chemical Thermodynamics and Information Theory with Applications 

FIGURE 3.10 Composite systems and thermodynamic uncertainty. The meter attached to the left compartment registers a signal, depending on whether the neon atom is present or absent. The atom is free to drift between the compartments. The lower panel shows an idealized probability density function. The effects of moving the piston right to left are considered in Exercise 3.12 at the end of the chapter. 

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