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Research concerning the relationship between the thermodynamic quantity entropy and both the origin and evolution of life began around the turn of the 20th century. In 1910 American historian Henry Adams printed and distributed to university libraries and history professors the small volume A Letter to American Teachers of History proposing a theory of history based on the second law of ...
Owing to these early developments, the typical example of entropy change ΔS is that associated with phase change. In solids, for example, which are typically ordered on the molecular scale, usually have smaller entropy than liquids, and liquids have smaller entropy than gases and colder gases have smaller entropy than hotter gases.
The statistical definition of entropy defines it in terms of the statistics of the motions of the microscopic constituents of a system — modelled at first classically, e.g. Newtonian particles constituting a gas, and later quantum-mechanically (photons, phonons, spins, etc.). The two approaches form a consistent, unified view of the same ...
This law of entropy increase quantifies the reduction in the capacity of an isolated compound thermodynamic system to do thermodynamic work on its surroundings, or indicates whether a thermodynamic process may occur. For example, whenever there is a suitable pathway, heat spontaneously flows from a hotter body to a colder one.
The energy and entropy of unpolarized blackbody thermal radiation, is calculated using the spectral energy and entropy radiance expressions derived by Max Planck [61] using equilibrium statistical mechanics, = (), = ((+) (+) ()) where c is the speed of light, k is the Boltzmann constant, h is the Planck constant, ν is frequency ...
Mathematically, the absolute entropy of any system at zero temperature is the natural log of the number of ground states times the Boltzmann constant k B = 1.38 × 10 −23 J K −1. The entropy of a perfect crystal lattice as defined by Nernst's theorem is zero provided that its ground state is unique, because ln(1) = 0.
Entropy is one of the few quantities in the physical sciences that require a particular direction for time, sometimes called an arrow of time. As one goes "forward" in time, the second law of thermodynamics says, the entropy of an isolated system can increase, but not decrease. Thus, entropy measurement is a way of distinguishing the past from ...
Here, U is internal energy, T is absolute temperature, S is entropy, P is pressure, and V is volume. This is only one expression of the fundamental thermodynamic relation. It may be expressed in other ways, using different variables (e.g. using thermodynamic potentials). For example, the fundamental relation may be expressed in terms of the ...