Von Mangoldt function: Difference between revisions

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'''Residual entropy''' is the difference in [[entropy]] between a non-equilibrium state and crystal state of a substance close to [[absolute zero]].  This term is used in [[condensed matter physics]] to describe the entropy at zero kelvin of a [[glass]] or [[plastic crystal]] referred to the crystal state, whose entropy is zero according to [[Third law of thermodynamics]]. It occurs if a material can exist in many different states when cooled. The most common non-equilibrium state is vitreous state, [[glass]].  
 
A common example is the case of [[carbon monoxide]], which has a very small [[Molecular dipole moment|dipole moment]]. As the carbon monoxide crystal is cooled to absolute zero, a few of the carbon monoxide molecules have enough time to align themselves into a [[perfect crystal]], (with all of the carbon monoxide molecules oriented in the same direction). Because of this, the crystal is locked into a state with <math>2^N</math> different corresponding [[microstate (statistical mechanics)|microstates]] (<math>2^N</math> permutations), giving a residual entropy of <math>S=Nk\ln(2)</math>, rather than zero.
 
Another example is any amorphous solid ([[glass]]). These have residual entropy, because the atom-by-atom microscopic structure can be arranged in a huge number of different ways across a macroscopic system.
 
==History==
One of the first examples of residual entropy was pointed out by [[Linus Pauling|Pauling]] to describe water [[ice Ih|ice]]. In water, each oxygen atom is bonded to two hydrogen atoms. However, when water freezes it forms a tetragonal structure where each oxygen atom has four hydrogen neighbors (due to neighboring water molecules). The hydrogen atoms sitting between the oxygen atoms have some degree of freedom as long as each oxygen atom has two hydrogen atoms that are 'nearby', thus forming the traditional H<sub>2</sub>O water molecule. However, it turns out that for a large number of water molecules in this configuration, the hydrogen atoms have a large number of possible configurations that meet the 2-in 2-out rule (each oxygen atom must have two 'near' (or 'in') hydrogen atoms, and two far (or 'out') hydrogen atoms). This freedom exists down to absolute zero, which was previously seen as an absolute one-of-a-kind configuration. The existence of these multiple configurations that meet the rules of absolute zero{{Clarify|date=March 2012}} amounts to randomness, or in other words, entropy. Thus systems that can take multiple configurations at or near absolute zero are said to have residual entropy.
 
Although water ice was the first material for which residual entropy was proposed, it is generally very difficult to prepare pure defect-free crystals of water ice for studying. A great deal of research has thus been undertaken into finding other systems that exhibit residual entropy. [[Geometrical frustration|Geometrically frustrated]] systems in particular often exhibit residual entropy. An important example is [[spin ice]], which is a geometrically frustrated magnetic material where the magnetic moments of the magnetic atoms have Ising-like magnetic spins and lie on the corners of network of corner-sharing tetrahedra. This material is thus analogous to water ice, with the exception that the spins on the corners of the tetrahedra can point into or out of the tetrahedra, thereby producing the same 2-in, 2-out rule as in water ice, and therefore the same residual entropy. One of the interesting properties of geometrically frustrated magnetic materials such as spin ice is that the level of residual entropy can be controlled by the application of an external magnetic field. This property can be used to create one-shot refrigeration systems.
 
==See also==
*[[Ice Ih#Proton disorder|Proton disorder in ice]]
*[[Geometrical frustration]]
 
{{DEFAULTSORT:Residual Entropy}}
[[Category:Thermodynamic entropy]]

Latest revision as of 07:05, 2 December 2014

But it seems like no matter how much your diet or exercise, they're still there. Copyright (c) 2013 Alex Jacob - Article Source: more secrets treating cellulite, please click here today. A Saran wrap might be helpful to wrap it for a few minutes. Follow these guidelines for the next few months and soon you'll be happily packing your bathing suit and shorts for a tropical winter vacation. This then means they are push upwards beneath the skin thereby the ugly looking lamps in addition to bumps.

Instead, consuming plenty of water and also enjoying sufficient physical exercise to help turn the cellulite fatty tissue right into electricity is the most effective method to go, as well as there ARE all-natural treatment alternatives to aid in boosting body's appeal along the way. Numerous aspects can contribute to the development of cellulite, consisting of body structure, hormone imbalances, diet, way of life, flexibility in the skin, and blood circulation system concerns. With the latter, you can enjoy the benefits of this weight busting, cellulite treatment at the comforts of your home. Another factor responsible for the bumpy skin is retention of water during pregnancy, which is a natural phenomenon. While many people want to see their cellulite reduced or, better yet, eliminated, the prohibitive costs and inherent risk of these procedures leaves most of these people at a loss for what to do.

Lack of exercise, bad dietary habits, and poor circulation are equally to be blamed for this undesirable condition. If you know that, it'll be easier to help you get rid of cellulite the vegetarian way. These three are definitely the simple for of cellulite exercises, It is advisable to visit exercise to get rid of cellulite for more thorough guide on exercising to eliminate cellulite. The bottom line, however, is that if you really want to get rid of that dimpled fat, you will have to reduce your weight and do some cellulite exercises. Normal water is beneficial because it improves metabolic rate and it's also good for the epidermis.

But, the revolutionary new cellulite treatment called Cellulaze has swiftly established itself as the only answer that may remove the vast majority of evident cellulite. Cellulite massagers will function by breaking down the fat deposits which are situated beneath your skin. Some people do report a benefit but it is unfortunately short lived and only temporary. An effectual HGH releaser will help in stimulating the pituitary gland to produce more human growth hormones. Using skin thinning creams, like steroid, on areas of cellulite will make the cellulite more obvious.

Adult men don't have cellulite, besides when they endure from hormonal ailments (diminished manufacturing of testosterone and enhanced production of female intercourse hormones). To start off, you need to make a daily dietary menu to follow so you will consistently eat the right foods that will help you remove fat from your skin tissue. So basically, if you can avoid caffeine, you will be able to avoid cellulite build up to some degree. Others say that it is normally the condition of many women. Something that you can apply in the privacy of your own home so you don't have to feel self conscious but can enjoy the good feeling you'll achieve from looking better and feeling better about yourself.

If you have any sort of inquiries regarding where and just how to use laser cellulite treatment, you could call us at our site.

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