Is there a relationship between temperature and entropy for crystals?

[wangasu]

Textbook says that entropy is a measure of energy unavailable to do work. For a crystal, entropy will increase with temperature, which, according to the definition, seems to mean that the useless energy increases. but, on the other hand, the quantity of heat energy available to do work depends on the temperature difference of two heat resources, and, thus, does not necessarily increase. I think I might mix something up here, and could you help me out?

 

[Danger]

Unless I'm missing something here, I suspect that your textbook was written by an idiot. From everything that I've learned, entropy is the disorder of a system. ie: complexity will revert to simplicity at its earliest opportunity. I can't for the life of me figure out what a crystal has to do with it.

 

[wangasu]

Unless I'm missing something here, I suspect that your textbook was written by an idiot. From everything that I've learned, entropy is the disorder of a system. ie: complexity will revert to simplicity at its earliest opportunity. I can't for the life of me figure out what a crystal has to do with it.

You might be wrong.. Generally, there are two main manifestations about entropy, one being a measure of the disorder of a system, and the other a measure of the amount of energy which is unavailable to do work. sometimes, entropy is also said to be a measure of the multiplicity of a system. If you had searched on line by simply entering 'entropy', you would have seen those.

 

[Danger]

I've never heard of the 'multiplicity' or the 'lack of available energy' things, and I never look for anything online outside of PF. There's way too much BS out there, and I know that I'll get the real goods here. It's time for someone with more knowledge to weigh in on this issue.
I don't mean that in a confrontational way; I'm at the limit of my education here, and there are others far more qualified to contribute.

 

[Galileo]

I`m sure the 'useful avaible energy' definition exists in some textbooks, but is from a physical point of view quite inadequate.
True, if we were able to use heat energy to do work we would decrease the entropy of the system which is forbidden, and vice versa. So you can see the vague 'equivalence' of the two views.
The pragmatic understanding of entropy as useable energy is useful in some cases when we worry about technical applications such as the efficiency of steam engines, for which thermodynamics was first invented.

I would equate entropy with a measure of realizable states of the system (precisely, the logarithm of the number of available states) and not to disorder although it suffices is most cases.
The physical reason entropy always increases is simply because the system will move to a state with the largest number of corresponding microstates. Not because it wants to, but because it is more likely. There exist much much more of those states. Disorder is more probable than order (as the ministers of education seem to know well). This is why the 'usefulness of energy' interpretation doesn't suffice.
Heat flows from a hotter body to a colder body because it increases the total entropy of the system (i.e. it is extremely unlikely to do otherwise), not because nature wants to frustrate our attempts to build an efficient steam engine.

 

[Sir_Deenicus]

Unless I'm missing something here, I suspect that your textbook was written by an idiot. From everything that I've learned, entropy is the disorder of a system. ie: complexity will revert to simplicity at its earliest opportunity. I can't for the life of me figure out what a crystal has to do with it.

I will not say that you are wrong as I do not believe it is my place to make such dunciations, however, I will say that it is my strong belief that you make a few incorrect statements. The first point is that while entropy can be considered to be a measure of disorder in a system in (or near) thermodynamic equillibrium, it is most certainly not the disorder of a system. Nor is it necessarily a direct indication of http://www.econ.iastate.edu/tesfatsi/hogan.complexperplex.htm" .

Entropy is more or less a measure of the number of available configurations or states for a given system. For example, in a box filled with a gas, it is easier to extract work from a gas which is located all to one side versus one with more possible available configurations, i.e. evenly distributed throughout the box. For example:

A state of higher entropy with more possible states
|o          o  |
|     o      o |   
| o         o  |

Lower entropy with work extractable when gas expands
|            o |
|        o o o |   
|         o o  |

For a crystal with a high "temperature" or one with a large degree of motion in its consituent molecules there exists more entropy as there are more possible states, which implies an interaction with some other system and an exchange of energy.

Entropy increases always, or atleast remains the same for any (two or more) systems for which mixing of energy occurs till thermal equilibrium is reached.