Everything about Thermodynamic Limit totally explained
In
physics and
physical chemistry, the
thermodynamic limit is reached as the number of particles (
atoms or
molecules) in a system
N approaches infinity — or in practical terms, one mole or
Avogadro's number ≈ 6 x 10
23. The
thermodynamic behavior of a system is asymptotically approximated by the results of
statistical mechanics as
N → ∞, and calculations using the various
ensembles converge. Theoretically, this concerns manipulating
factorials arising from
Boltzmann's formula for the
entropy,
S =
k log
W, by using
Stirling's approximation, which is justified only when applied to large numbers. But it probably has an empirical basis as well. Ordinary thermodynamics may not apply to collections of only a few atoms or molecules.
In some simple cases, and at
thermodynamic equilibrium, the results can be shown to be a consequence of the additivity property of
independent random variables; namely that the
variance of the sum is equal to the sum of the variances of the independent variables. In these cases, the physics of such systems close to the thermodynamic limit is governed by the
central limit theorem in probability.
For systems of large numbers of particles, the genesis of macroscopic behavior from its microscopic origins fades from view. For example, the
pressure exerted by a
fluid (gas or liquid) is the collective result of collisions between rapidly moving molecules and the walls of a container, and
fluctuates on a microscopic
temporal and
spatial scale. Yet the pressure doesn't change noticeably on an ordinary macroscopic scale because these variations average out.
Even at the thermodynamic limit, there are still small detectable fluctuations in physical quantities, but this has a negligible effect on most sensible properties of a system. However, microscopic spatial density fluctuations in a gas scatter light (which is why the sky is blue). These fluctuations become quite large near the
critical point in a gas/liquid
phase diagram. In electronics,
shot noise and
Johnson-Nyquist noise can be measured.
Certain
quantum mechanical phenomena near the
absolute zero T = 0 present anomalies; for example,
Bose-Einstein condensation,
superconductivity and
superfluidity.
It is at the thermodynamic limit that the additivity property of macroscopic
extensive variables is obeyed. That is, the entropy of two systems or objects taken together (in addition to their
energy and
volume) is the sum of the two separate values.
Further Information
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