Question on thermodynamics

[Illiad]

1.From a textbook, I found out that a refrigerator moves more energy from a cold reservoir to a hot reservoir than it comsumes. Similarly a heat engine moves more energy from a cold reservoir to a hot reservoir than it consumes. Based on the attached diagram, the whole system would work as a refrigerator transfering net heat of Ql from the cold reservoir to the hot reservoir. But the textbook also says that the system won't work because it would be in clear violation of Clausius statement, which says

 

'it is impossible to construct a device that operates in a cycle and produces no effect other than the transfer of heat from a lower temoerature body to a higher temperature body'

 

but it didnt go beyond that. I know it is impossible without a Q input but I cant find fault with the diagram. Like perpetual machines, the whole thing seems to work on paper.

 

2. About entrophy. For a system A and B in a isolated system, with A warmer than B, if both comes into contact, A will transfer heat to B resulting in B getting more 'disordered' and A getting more ordered. My question is, does more disordering occurs than ordering or

the disordering and ordering are of equal magnitude? what is ordering and disordering anyway? I can't phantom it in my head

Edited August 8, 2010 by Illiad
arrow in diagram pointing the wrong way

[Qfwfq]

Like perpetual machines, the whole thing seems to work on paper.

The trouble is that, in your diagram, the energy [imath]Q_h[/imath] is thermal but you have it magically becoming work which isn't thermal.

 

About entrophy. For a system A and B in a isolated system, with A warmer than B, if both comes into contact, A will transfer heat to B resulting in B getting more 'disordered' and A getting more ordered. My question is, does more disordering occurs than ordering or

the disordering and ordering are of equal magnitude? what is ordering and disordering anyway? I can't phantom it in my head

If the absolute temperatures of A and B are [imath]T_{\rm A}[/imath] and [imath]T_{\rm B}[/imath] then the total entropy variation is [imath]\frac{Q}{T_{\rm B}}-\frac{Q}{T_{\rm A}}>0[/imath] because the larger denominator makes the second term smaller.

 

Consider a block of iron sitting on the top of your desk. The atoms it is made of are shaking about and at room temperature their average speed is incredibly huge, but the block is sitting still. This means that the atoms are going in all kinds of diractions and each one is going one way and then another. If they were all going at the average speed and in the same direction it would be an orderly motion of the whole block but it wouldn't be at the same temperature; the more equal their velocities were, the colder it would be. The same energy would be less thermal and more macroscopic mechanical.

 

If the block knocks against another rigid surface, the kinetic energy gets thermalized. It's easy to make this happen, what's a problem to achieve is the opposite. For this reason, entropy is a concept related to statistics and information theory. A gas could be separated into hot and cold by simply opening and closing pores in a membrane, at the exact right times in such a way as to let faster molecules go one way and slower one the opposite, but of course this would require a mighty amount of detailed info about each molecule's motion. This is how an omniscient being (called Maxwell's demon) could violate the 2nd principle but, if the necessary knowledge isn't magically available, then any practical, physical way of achieving the separation without expenditure of work winds up increasing entropy elsewhere or else fails.

[Illiad]

I've stumbled upon Maxwell demon before while looking up the second law of thermo on wiki.

Is the 2nd law is merely an obstacle we cannot overcome yet or a fact of nature?

Some argued that the demon would need energy to process information and close/open the door, so the second law stills hold, they say.

what if a membrane that works sort of like cornstarch and water is used?

If the absolute temperatures of A and B are and then the total entropy variation is because the larger denominator makes the second term smaller.

This very simple explanation tells me I have think things more throughly first. Thanks =D

[Qfwfq]

lol yes, it wasn't all that difficult to see why entropy increases.

 

Is the 2nd law is merely an obstacle we cannot overcome yet or a fact of nature?

It is a fact of mathematics. It's kinda like not having enough information to "calculate" which lotto numbers are going to come out next, but the statistics for a macroscopic system of molecules are even more overwhelming.

 

Brownian motion is a large number of brief, small violations of the 2nd principle. Of course they average out to zero. If the demon just leaves the hole in the membrane open, whenever a molecule goes through that's either much faster or much slower than the average, you can say "Aha!" but, of course, molecule after molecule, you can expect it'll average out in the end.

 

Some argued that the demon would need energy to process information and close/open the door, so the second law stills hold, they say.

This is kinda the difference between a practical, physical device and the true (but inexistent) demon that "just knows" without any processing. We certainly can't make such a demon, we can only make devices that rely on some physical interaction. However, the hypothetical demon argument shows that it's a matter of probability: instead of making a demon that does know, replace it with a tiny chimp... Just as in the monkey-at-the-keyboard scenario, for any size of violation there is some tiny probability of it occuring in a given run.

 

what if a membrane that works sort of like cornstarch and water is used?

I'm just guessing that you mean a high viscosity contrivance, where a mixing can be fairly well reversed. This, in short, is because it isn't thermal agitation that prevails but instead the macroscopic mechanical driving force. It would be a daunting task to exactly reverse the momentum of every single molecule of a system, in such a way as to make a thermal process go backwards! In principle, at least in classical mechanics, that's all there is to it. ;) Edited August 9, 2010 by Qfwfq