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Entropy and Heat Capacity have the same units. Connection? Redundancy? 
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#1
Jun2212, 09:10 PM

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Given that heat capacity is a ratio of change of energy over change of temperature, while entropy is a change of energy over absolute temperature...
I was wondering if there is any basis for the idea that energy will tend to flow from media having low heat capacity to media having high heat capacity, such that the imported energy becomes colder as a result of the higher heat capacity of the destination medium relative the medium departed. See a table of specific heat capacities for different materials: http://en.wikipedia.org/wiki/Heat_ca...eat_capacities In other words, energy of an object could be thought of as getting hotter or colder due to heat capacity variations. As a result of such a energy transfer (=ΔE), the entropy would increase as result of ΔE/t increasing (i.e. 0 < ΔE/t_(cold, final)  ΔE/t_(hot, initial)), where ΔE specifically would refer to the energy that is transferred. In this sense, entropy is not so much a flow, but rather an intensity like heat capacity. And what if, in the end, if we account for entropy changes by such transfers of energy, couldn't that concept of pinning thermodynamic state variables to energy as opposed to pinning them to boundarydefined systems, as is almost always assumed in traditional teaching, make entropy and heat capacity oneandthesamething? It is also known that there are different heat capacities for a given substance based on: * constant volume, as in an isochoric process * constant pressure, as in an isobaric process So depending on the present process occurring in a given thermodynamic cycle, the direction of energy flow that would increase entropy could change  or even reverse. Conversely, one could flip the perception around and imagine that entropy itself flows from systems of low heat capacity to those of high heat capacity, causing the heat capacity of the systems which they flow into to increase, while causing the heat capacity of systems they are leaving to decrease. Certain materials have different effects on the flow of heat, so couldn't understanding of that be aided by the idea that entropy and heat capacity are intimately connected? Could the ability to engineer extreme differences in heat capacity facilitate extraction of ambient thermal energy? If there can be a heat capacity for constant pressure and a heat capacity for constant volume, wouldn't the concept of pinning thermodynamic state variables to energy as opposed to pinning them to boundarydefined systems, as is almost always assumed in traditional teaching, suggest the existence of a temperature for constant pressure [dynamics] and a temperature for constant volume [statics], so maybe it is related to the relation between dynamic pressure vs. static pressure: http://www.physicsforums.com/showthread.php?t=169660? 


#2
Jun2312, 07:53 AM

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Entropy and Heat capacity are, indeed, related concepts.
I think you want the statistical mechanics description of these things to understand your questions. What you don't want to do is think of the energy as having a temperature. An object may have thermal energy as well as temperature... two properties which are related. 


#3
Jun2312, 11:51 AM

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#4
Jun2312, 03:18 PM

P: 5,462

Entropy and Heat Capacity have the same units. Connection? Redundancy?
Entropy (unlike energy) does not 'flow from one place to another'. In the above example the take up of latent heat on say melting goes into a rearrangement of the melting system such that it has greater entropy. The heat supplied to cause the melting may also result in greater entropy of the surroundings if it is the result of a say a chemical reaction such as burning a fuel. So the entropy does not flow from surroundings to system but increases in both. The overall entropy of the universe may increase by such a process. 


#5
Jun2312, 03:50 PM

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The ocean has more entropy because of two things: 1: There is more heat energy in the ocean (Joules) 2: The heat energy in the ocean is at lower temperature (Kelvins) 


#6
Jun2312, 03:59 PM

P: 1,011

I can think of a van as having 1 passenger. Such a concept makes sense. I can state that, "A van has 1 passenger." That statement is not made incomprehensible or meaningless by the notion of a Mini Cooper which has three passengers on board. It means something, and that meaning makes sense. It is not unreasonable to think of such a case. http://chemistry.about.com/od/worked...leProblem.htm 


#7
Jun2312, 04:06 PM

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If so, why is the same not the case for temperature? If not, then why does it make sense for a system to have entropy, while the same is not true for energy. Also, why does it make sense to talk about the temperature of a system, and the temperature of an object, but not the temperature of an energy? 


#8
Jun2312, 04:36 PM

P: 5,462

I will try one more time.
Energy, entropy and temperature are different physical quantities or properties or variables. Temperature is an intensive property. Entropy and energy are extensive properties. (Pressure, temperature , molar volume, specific heat, refractive index are examples of intensive properties. Mass, volume, enthalpy, entropy, heat capacity, pressure_volume product are extensive examples.) The physical dimensions (units) of energy or entropy preclude them "having a temperature". An example property that does have a temperature is boiling point. The same goes for "energy having an entropy" Both are nonsensical notions. 


#9
Jun2312, 05:12 PM

P: 1,011

Using your contrived argument, you would also conclude that: "1 kg of water doesn't have a boiling point, because 1 kg of water is 1 kg of mass, 1 kg of mass is an extensive property, and an extensive property cannot have an intensive property such as a boiling point." That to me sounds a bit ludicrous. 


#10
Jun2312, 05:27 PM

P: 5,462

Take soldering iron (specific heat about 0.5) heat it and apply to solid solder (specific heat about 0.15). Heat flows from the iron to the solder and the solder melts, although the heat capacity of the iron is more than 3 times that of the solder. 


#11
Jun2312, 05:46 PM

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#12
Jun2312, 05:48 PM

P: 5,462

Heat flows (spontaneously) from a body with a higher temperature to one with a lower temperature.
That is one version of the second law of thermodynamics, due to Clausius. 


#13
Jun2312, 05:57 PM

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Let's take another simple example.
Liquid water has about 10 times the specific heat (5) of the iron in the previous example. Heat the iron to 180°C and dip it into the water at 25°C. Yes the heat will flow from the iron to the water, as you said. Now cool the iron to 5°C and again dip it into the water. Heat will now flow from the water to the iron. What's changed other than the direction of heat flow? Thermodynamics is quite clear about this. Temperature (difference) is the property which determines the direction of the heat flow. Nothing else. 


#14
Jun2312, 05:58 PM

P: 1,011

Energy > Various heat capacities > Temperature differences > Heat flows 


#15
Jun2312, 06:13 PM

P: 5,462

Heat capacity varies with temperature. When you have a better understanding of thermodynamics fundamentals you will be able to explore the reasons for this variation. But you need to come to terms with the basics first, rather than argue with the second law. 


#16
Jun2312, 06:21 PM

P: 1,011

"Heat capacity varies with temperature" is equivalent to saying "temperature varies with heat capacity". "Varies" is an associative term. What explains the difference of heat capacity between lead and gold (i.e. what is it caused by)? It's obviously not the temperature. 


#17
Jun2312, 06:21 PM

P: 546

Heat capacity is actually an extrapolation of a more general statistical expression. From Hill's statistical thermodynamics I derived this expression for C_{V}. If you have the book I used eqns [25], [21], and [111]. Of course, there are probably better definitions but this is as far as I've gotten in the text so far.
[itex] C_V = ( E (\sum_j E_{j}e^{E_{j}/{kT}} /{ \sum_j e^{E_{j}/{kT}} }) )^{2}/{kT^{2}} [/itex] where E is the energy of the system k is the boltzmann constant T is temperature E_{j} is the energy of an individual molecule in the system (a function of N,V for the canonical ensemble) So if you really wanted to you could sum over the energy this way, knowing the temperature distribution to solve for the heat capacity. DISCLAIMER: I am a novice at statthermo! 


#18
Jun2312, 06:30 PM

P: 5,462

But what I can do is take a block of material and set its temperature. Nature does not force a temperature on me. Nature, however does force a heat capacity on me, I cannot set a heat capacity, which is why I looked up the values I posted earlier in Kaye and Laby. 


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