Thermal entropy

and molecules vibrate about their mean position. This vibration is a function of temperature. The entropy associated with this vibration is called thermal entropy, Sp. From Equation 18.18, it follows that  

Substituting for dq from Equation 18.1, we get, for change of thermal entropy. Equation 18.27. 

The change in thermal entropy at constant pressure can be written as  

or molecules can vibrate about their mean position. Einstein considered them as simple harmonic oscillators. Let us consider a mole of such oscillators. Let the frequency of oscillation be v. The thermal entropy per mole is given by  

If the frequency changes from say v to v, then the change in thermal entropy is given by Equation 18.33. 

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The values of S° represent the virtual or thermal entropy of the substance in the standard state at 298.15 K (25°C), omitting contributions from nuclear spins. Isotope mixing effects are also excluded except in the case of the H—system. 

In this approximation it is assumed drat die endialpy of exchange is equal to the energy of exchange, and the thermal entropy of exchange is equal to zero. Both of diese imply that there is no change in heat capacity when this exchange is carried out, which is not normally the case, although the effect is small. 

There is also a small contribution from thermal entropy, but this can be neglected. 

The case is unusual and not quite correct, as no energy has been put into it since its initial creation, so that it is not in a true cyclic steady state. Friction, no matter how small, will cause the flow to stop it must produce some thermal entropy. Unlike a true cyclic system it is not truly time-independent and would require energy input to be so. We treat next a physical system where energy input is clear. 

Fig. 3.14. The total thermal entropy drive which underlies the energy connection between the cycling of elements in life and environment while energy is degraded.

Note All flow runs with thermal entropy increase toward a final system. 

Throughout the whole of this evolution it is the ecosystem which evolves with all kinds of chemotypes. The whole of biological evolution is but advancing the effect of high-frequency energy applied to material and released as low-frequency heat - an ever-increasing rate of thermal entropy production. 

The unattainabiiity formulation of the Third Law of Thermodynamics is briefly reviewed in Sect. 2.1. It puts limitations of the quest for absolute zero, and in its strongest mode forbids the attainment of absolute zero by any method whatsoever. But typically it is stated principally with respect to thermal-entropy-reduction refrigeration (TSRR). TSRR entails reduction of a refrigerated system s thermal entropy, i.e., its localization in the momentum part of phase space (in momentum space for short). The possibility or impossibility of overcoming these limitations via TSRR is considered, in Sects. 2.2. and 2.3. with respect to standard TSRR, and in Sect. 2.4. with respect to absorption TSRR. (In standard TSRR, refrigeration is achieved at the expense of work input in absorption TSRR, at the expense of high-temperature heat input.)... 

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