# Heat vs. temperature vs. energy

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*This discussion page is not really an article. One day these things might get reorganized, but this whole wiki is for design discussions.*

## Essay on "Heat vs. temperature vs. energy" (feel free to revise it)Edit

Thermodynamics is a tough subject. The fact that centuries after the facts were known, we still don’t have an adequate supply of heat and work, shows just how hard it is to understand. Here I want to explain a common misconception: energy doesn’t go away after it is “used,” and when a kilojoule of heat flows between two objects, the amount of energy transferred is the same (still a kilojoule) regardless of the temperature of the objects.

*When a quantity of energy is used and the temperature is lowered the entropy has increased, and it is no longer as useful as when it existed at the higher temperature.*

- Temperature is a property of a system of particles and is only defined when the system is in thermodynamic equilibrium. Temperature is not a property of energy. One cannot assign a temperature to a unit of energy. Instead, temperature predicts the distribution of energies which will be observed in a system of particles. Usually the Maxwell-Boltzman distribution applies, with a peak such that the most likely energy for an individual particle is kT.

- If we measure temperature in joules instead of kelvins (multiplying by Boltzman's constant to convert) then the temperature is simply the most likely kinetic energy (measured in the rest frame of the system) of a particle selected at random from that system.

If many people had a firm understanding of thermodynamics, surely someone would have realized how valuable an effective low delta-T heat engine would be, and would have already invented it. Instead, we spend billions on nuclear fission and fusion, and continue to burn fossil fuels to get heat and work when we could take the heat and work from ambient temperature differences.

*That inability to extract useful mechanical work from low temperatures is precisely the problem. The Carnot efficiency is an unalterable fact of thermodynamics. This severly limits the amount of said useful work that can be obtained regardless of the quantity of energy available between the two temperatures.*NotSCar 21:31, 24 September 2006 (UTC)

- If the Carnot efficiency is 5%, but I have 20 times the heat flow, then I get the more work from that 20 units of heat flow than I can get from 1 unit of heat flow with Carnot efficiency of 99%. But in this case, I have say one billion times more heat flow (heat from ambient temperature air vs. heat from direct solar ratiation or from fuel or whatever), with those same Carnot efficiencies. I get 200 million times more energy from the 5% efficient process than from the 99% efficient process.Archimerged 18:30, 26 September 2006 (UTC)

Heat, temperature, and energy are all closely related. Heat and energy are measured in joules. Temperature is measured in Kelvins, but Boltzmann’s constant (joules per Kelvin) converts any temperature to a related amount of energy.

The sun emits energy in the form of photons of various frequencies. The temperature of the solar surface is around 6000K. This means that fewer photons are needed to carry a given number of joules away from the sun than from a colder object.

Planck’s constant (joules per Hertz) converts photon frequency (Hertz, inverse seconds) to energy (joules).

## Comments Edit

Unless there have been some major changes in thermodynamics the amount of energy to be realized as useful work between two temperatures T sub h, the high temperature heat source and T sub l, the low temperature heat sink is limited to the maximum allowed by the Carnot efficiency. Because some has been converted to work and some is at the sink temperature, that total amount of energy is not as available as it was heretofore and consequently the entropy has increased.

Any LTD (low temperature difference) engine is subject to these limitation in addition to the practical problem of getting the maximum flow of heat into a given externally heated engine shell or system. There's the rub. NotSCar 2006-09-13 22:16:18

- Hi, NotSCar. Thanks for the comment. This page isn't really an article, it is just a verbatim copy of an couple of paragraphs written last January on a blog. Let's treat it like a discussion page. There have been no changes to thermodynamics, and LTD engines require very high efficiency to operate at all. It is quite easy to end up with a cold compression process that uses more energy than the hot expansion process produces. Then the engine requires input of work to make the cycle operate. However, the total amount of energy available at LTD is so vast that at least a few people ought to spend time thinking about how to convert some of it to work before it continues its journey from the sun out to the stars. Archimerged 04:18, 23 September 2006 (UTC)

Lets get our terms on a more rigorous footing. What do we mean by "Heat" or "Cool"? We heat coffee and cool iced tea. Neither is quantifiable. Temperature can be specified or quantified in degrees "C" or "K," "F" or "R." An amount or quantity of heat can be sepeified in various systems in BTU's, joules, and calories. Specify pressures in absolute terms to avoid confusion.NotSCar 20:59, 24 September 2006 (UTC)NotSCar

- Of course we are using SI units with temperature in kelvins (not "degrees K") and heat in joules. The amount of heat added to coffee or removed from iced tea is easily quantified by weighing the liquid and measuring the temperature before and after and using the known heat capacity. Archimerged 18:30, 26 September 2006 (UTC)

Archimedes, you glibly mention "I have say one billion times more heat flow (heat from ambient temperature air...") Question: How do you make this abundance of thermal energy available for use or make practical use of it? Granted the atmosphere is a vast reservoir of energy but it is only available for use at it current temperature and whatever thermal sink temperature is available thus limiting the amount of energy available over any specified time or at a rate of flow. Thermal energy flow from the sun to earth has little to do with how we realize or use that portion which is stored in "ambient temperature air." Perhaps you can clarify the matter in simple terms for a simple minded person like myself.NotSCar 02:06, 28 September 2006 (UTC)

- The purpose of this wiki is to discuss that very question. You start by saying you don't see any way to do it. Then you have given up before even trying. The limitations are less fundamental than you think. Granted, the machines required will be very large and expensive. So is an oil field. Archimerged 21:13, 29 September 2006 (UTC)