A Slightly More Formal Proof (For Dummies)

Here are the rules :

  1. Heat flows from warmer objects to cooler objects
  2. Heat can not flow from a cooler object to a warmer object

Therefore, if the temperature of the cooler object increases – the only way to maintain the condition of rule 1 is for the temperature of  warmer object to also increase.

People are making the mistake of not understanding the difference between heat and temperature. The diffusive heat flow between a 30 degree location and a 20 degree location is the same as the diffusive heat flow between a 70 degree location and a 60 degree location.

BTW – I used to model heat flow for a living. Feel free to make a fool of yourself though.

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75 Responses to A Slightly More Formal Proof (For Dummies)

  1. Ben Vorlich says:

    Question for clarification, is any energy entering the system you describe?

  2. R. Shearer says:

    I think this applies to absolute temperature. Further, pressure, change of state and other variables must be taken into account.

  3. PJ London says:

    OK I will make an idiot of myself.
    Two objects , a has a certain mass, composition etc. and has a Temperature of x deg (energy in the form of heat?)
    Object b has a mass etc, and a temperature of y being less than x.(i,e less energy in the form of heat)
    Object b now absorbs heat (energy) and increases temperature to z deg (greater than y but less than being less than x),
    Why does object a have to experience an increase in temperature?.
    Assume no external energy source, why would energy (heat) not transfer from object a to object b causing a decrease in temperature of a and increase in temperature in object b?
    Unless there are other conditions to your original picture, it makes no sense to me.

    • Curt says:

      “Assume no external energy source”

      The sun is an external energy source for the earth.

      With a fundamentally constant input from the sun, if you reduce the heat transfer from earth to a colder ambient (space), its energy and therefore temperature increase until earth’s power output again matches the input from the sun.

    • Mat Helm says:

      PJ,
      I think you, like I did (until I was half way into a reply agreeing with you), may have missed the “The only way to maintain the condition of rule 1″part. The “Maintain” being the key word there. As in continuous….

  4. Steve Case says:

    I objected to this phrase from your [My Position] post:

    Warm greenhouse gases in turn radiate more longwave radiation, half of which radiates downwards towards Earth and warms the Earth’s surface further.

    Warms something further means an increase in temperature in my book.

    • Tel says:

      You have to remember that the Earth surface is not steady state, it cycles, and from a climate point of view, only two measurements exist: the maximum temperature during the day, and the minimum temperature in the early morning. That’s it, all other temperature gets ignored.

      The surface station always cools at night (heat flows out of the warn Earth into cold space) but on humid nights will cool more slowly, thus the all important minimum temperature reading will be warmer than on clear dry nights. This has a “warming” effect when the average temperature is calculated.

      There are also some cases were low cumulus clouds can move in and be warmer than the surface, admittedly not the typical situation. Clouds contain stored energy as latent heat so they can maintain their temperature by gradually consuming that stored energy as the water condenses.

  5. mkelly says:

    Therefore, if the temperature of the cooler object increases – the only way to maintain the condition of rule 1 is for the temperature of warmer object to also increase.
    +++++

    True if and only if you are trying to maintain a specific difference or specific flow. Your example of 30 to 20.
    Rule 1 is still intact if the 20 increases to 25 or 28 or 22 as 30 is still higher. Less heat will flow as the 20 increases up to but not including 30.

  6. Timo Soren says:

    Please explain your terms for the following experiment and results. In a vacuum two cubes of a a like material are placed, say one at 1000C the other at 50C. Assume no background radiation. As time passes, both objects emit radiation and hence are cooling through radiation, but not conduction or convection. Can one not imagine a scenario where the cooler objects radiation is impaired (insulation) on all sides but the one facing the other object. That it is radiating substantially less into space than the hotter object AND that the radiation aborbed by the cooler object on the non-insulated side is greater than the radiation emitted and hence that cooler object is being heated. Hence, the warmer object will cool and the cooler object will warm.

    • R. Shearer says:

      There are obviously some complexities that perhaps Steve did not want us to consider for the sake of a simplicity. Let me get a beer from the fridge, whose inside is alway cooler than the outside when powered, and I’ll think about it.

  7. kentclizbe says:

    Tony,

    It seems that your earlier analogy of a human body being “warmed” by a blanket did not clarify, but rather confused the issue.

    A human body (as others pointed out) is a “heat machine.” The body, while alive, is turning chemical energy into heat.

    Thus, the blanket applied to the living body does NOT “warm up” the body, or “increase the heat.”

    The blanket reduces the heat lost from the heat-producing human body, and the body’s temperature then increases.

    Yes, the inner core temperature increases–but the increased heat is NOT from the blanket. The heat is from the body’s own chemical heat-machine, captured by the blanket’s insulation–NOT lost to the cold air.

    Applying this analogy to the topic we are all interested in–the Earth’s “Green-house gas” effect, there is a great disconnect. The Earth’s heat (discounting radioactive processes and other geothermal heat production) comes from an external source–the sun. Wrapping the Earth in a globe-sized thermal blanket would NOT increase the Earth’s temperature–there would be no heat-machine pumping out heat from within.

    I think this is where you’re getting push-back from AGW skeptics.

    Applying the (flawed) body-blanket analogy to the atmosphere-Earth relationship is not helpful to understanding whether/if CO2 heats the Earth’s atmosphere.

    Alarmists believe, in fact it is the fundamental belief in their catechism, that the more CO2 in our atmosphere, the hotter the Earth will be–inevitably causing the “runaway greenhouse effect.”

    Reality-denying alarmists’ body-blanket analogy would have a dead body boiling in its own juices as thicker blankets are piled on, creating “runaway body-warming.”

    Or as leading alarmist-reality-denier James Hansen says: “A runaway greenhouse effect means once the planet gets warmer and warmer, then the oceans begin to evaporate. And water vapor is a very strong greenhouse gas, even more powerful than carbon dioxide. So you can get to a situation where it just — the oceans will begin to boil, and the planet becomes so hot that the ocean ends up in the atmosphere.

    So, the problem that you’re running into is in that the explanatory analogies (“greenhouse,” or “body-blanket,” or “thermos”) are not valid or applicable to the Earth and CO2.

    Which leads to the other prong of the “greenhouse gas” debate you’ve been having–your assertion that H2O is the stronger of the greenhouse gasses–which mirrors Hansen’s warning of the ‘”runaway greenhouse effect” above.

    Which again contradicts actual physical observations here on real-Earth. Dry deserts (lacking H2O in the air) are hotter than maximally humid rain-forest regions. That’s a fundamental repudiation of the Hansen theory of H2O in the air causing runaway heating.

    Real-world observations appear to support the explanation that H2O provides a stabilizing effect–evaporation and condensation alternately cooling and warming–but overall stabilizing the temperature, NOT causing runaway heating.

    While there may be some whackos needling you constantly, I think that realists can agree that Hansen’s runaway greenhouse effect, triggered by man-made CO2, and dependent on evil H2O for the final stage of runaway heating–“boiling the oceans”–is an evil fantasy conjured up by the statist Politically Correct Progressives intent on destroying the fruits of our capitalist economy, and seizing control of our lives.

    Thanks.

  8. wayne says:

    “Therefore, if the temperature of the cooler object increases – the only way to maintain the condition of rule 1 is for the temperature of warmer object to also increase.”

    Only if the warmer object has some source of additional energy input, then yes, the warmer will get warmer up to re-equalization.

    Over multiple diurnals there is some solar input to the warmer object, I assume, so yes. Contraire, if you are speaking of just one single night with no energy input to the warmer object then no, temperature won’t rise but the warmer will cool more slowly.

    Careful not to leave out some very necessary words Steven. It all hinges on whether there is some source of additional energy flowing to and into the warmer object or not. Hope you programmed it that way.

    • Tel says:

      I think the assumption is that the Sun will always supply the same heat flow (i.e. power) to the Earth, regardless of what else happens.

    • Curt says:

      “The blanket reduces the heat lost from the heat-producing human body, and the body’s temperature then increases.”

      Let’s rework that:

      The [greenhouse gases reduce[] the heat lost from the [sun-powered] [earth], and the [earth’s] temperature then increases.

      • kentclizbe says:

        Curt,

        The difference in the body-blanket relationship and the Earth-GHG relationship is that the body is producing its heat INTERNALLY.

        That’s why that analogy is confusing and not applicable.

        The Earth’s source of heat is EXTERNAL, and is turned off half the time (night).

        In addition, the Earth has the stabilizing presence of water in its “blanket.”

        That’s where the analogy disintegrates. In the alarmists’ fevered dreams CO2 heats the Earth, evaporating water, which enters the atmosphere, and being a “greenhouse gas” heats the Earth even more, evaporating more water. This “runaway greenhouse” effect eventually “boils the oceans.”

        That is the fundamental terroristic threat that Hansen and his ilk make: CO2 triggers H2O evaporation–leading inexorably to “‘runaway warming” and “boiled oceans.”

        Which is nonsense.

        • Curt says:

          Kent: Internal or external does not matter here, thermodynamically speaking. What does matter is that it is a source of power separate from, and independent of, the power exchange between the two bodies.

          The sun “is turned off half the time” . Really??? Seriously, the short-term daily variation in sunlight at a given point on the earth matters very little for the long-term temperature average.

          The question as to whether there is any kind of “greenhouse effect” is very different from how sensitive that effect is to changes now.

        • kentclizbe says:

          Curt,

          The discussion of the heat source being internal was to demonstrate that a blanket wrapping a human body is not analogous to an atmosphere wrapping the Earth.

          The body is “warmed” by the blanket, NOT because the cold blanket heats the warm body. Rather the body’s temperature rises because the cold blanket slows the heat loss from the body, while at the same time, the body is creating its own heat–INTERNALLY.

          The Earth is NOT generating internal heat. Thus, the blanket-body analogy is really poor as a teaching/demonstration aid to explain the “greenhouse effect.”

        • Curt says:

          Kent: The whole point of the “greenhouse” metaphor is that both the real greenhouse glass and the metaphorical “greenhouse gases” let solar power in largely unattenuated, but significantly impede heat loss through insulation.

          In a real greenhouse, the insulation works by suppressing convective losses. In the atmosphere, the insulation works by suppressing radiative losses, so the metaphor isn’t perfect, of course.

        • kentclizbe says:

          Curt,

          Not applicable?

          The greenhouse metaphor is totally inapplicable to the Earth.

          The point I’m trying to make though, is that the body-blanket analogy is not applicable either.

          Tony’s earlier example of a blanket “raising the temperature” of a hypothermic human body does NOT apply to a blanket of “insulation” on the Earth.

          The blanket does not raise the temperature of the human body–it slows the loss of continuously supplied heat–WHICH IS BEING CREATED BY THE BODY’S HEAT-FACTORY.

          As the body burns chemical energy, it constantly creates heat. Without the blanket, in freezing conditions, the body’s internal heat is lost quickly, and the core temperature drops. When the blanket is wrapped around the living heat-factory, the loss of the continuously created heat to the colder air, is slowed. The slower loss of heat allows the heat-factory to warm the body.

          The example was provided as a case study of how “cold objects (blanket) heat warm objects (human body).”

          It does not demonstrate that at all.

          Wrapping a cold blanket around a hot rock will NOT raise the rock’s temperature. It will slow the rock’s loss of heat. But because the rock does NOT have an internal heat-factory, the rock’s temperature will NOT rise.

          Slowing heat loss is what the atmosphere does. If the atmosphere RAISED the temperature of the Earth, you would have a perpetual motion machine–with temperature bouncing higher and higher and higher until “the oceans boil,” as the con-man Hansen warns his acolytes.

          Since that hasn’t happened, doesn’t that falsify the hypothesis of “greenhouse gas” runaway heating?

        • Curt says:

          Kent: Are you really spending all this time on a semantic quibble?

          In cold conditions where a human would get hypothermia without insulation, wrapping the body in a blanket would lead to higher body temperature than without it. This is only possible because of the body’s metabolic power generation; it would just slow the cooling of a corpse.

          Is it really so wrong to say that wrapping a blanket around a hypothermic person “increased his body temperature”?

          Similarly, “wrapping the earth” in a metaphorical blanket of radiatively absorbent gases that reduce heat loss to the effective low temperature of space results in higher earth surface temperatures than would exist without it. But as with the person, this is only possible because of the separate power source of the sun. If there were no solar power input, it would just slow the rate at which the earth cooled to the temperature of its ambient.

          Again, is it really so wrong to say that the “blanket” of greenhouse gases around the earth “increase its temperature”? Does one really need to say every time that “given the constant solar power input, the presence of radiatively active “greenhouse” gases results in higher surface temperatures than would occur without them”?

      • Curt says:

        This was meant to reply to kentclizbe.

    • wayne says:

      Don’t let yourself think anything I said is tied to co2 concentration specifically, I can still find no evidence that co2 has any hand in our temperatures. In fact the opposite. I leave myself open to a number of explanations why the temperature is not rising and I don’t think it is going to continue to rise, the mean tenperature that is.

      The cooler object is the atmosphere and the warmer object is the surface and that has raised the mean temperature some +57°C per gallopingcamel (physicist) per Diviner probe of the moon to maybe as high as +134°C on a planet like ours with no atmosphere at all and no thermal inertia present. That is the real physics and those differneces need to be explained. The +33°C is rather meaninglessa and is just that input will equal output at some level and the temperature of that level if assumed dealing with a blackbody, which we are not, would spit out 33°C difference to match the OLR. So not only is that 33 rather meaningless, it is also not correct without a real measured emissivity and output per frequency band, even a graybody approximation will not do.

  9. theyouk says:

    At the (high) risk of sounding like a below-average turnip, I’d like to ask you to confirm–or better yet correct–my own understanding of something.

    On northern lakes during late spring and early summer…The only two sources of heat to raise the temperature are 1) the Sun shining into the water, and 2) any warm water flowing into the lake (never mind discharge from industry, motorboats, little kids peeing, etc.). A warm wind will NOT warm the water, no matter what the temperature difference between water and air, because as moving air interacts with water it will cause evaporation, thus removing heat from the lake.

    Is this correct, or am I removing all doubt that my middle name should be ‘Rutabaga’? Thanks for any insights!

    • Edmonton Al says:

      Sounds right to me…

    • Neal S says:

      There are simple answers and there are correct answers. Sometimes it is impossible to have both at the same time.

      All other things being equal, the warmer the water, the greater the evaporation rate.
      And all other things being equal, the higher the humidity in the air, the lower the evaporation rate. And all other things being equal, the greater the temperature difference between the air and the water, the greater the chance of the air warming the water. Air pressure may be a factor as well as higher pressures will reduce evaporation.

      So if the air is dry enough and the temperature difference low enough and the water warm enough, then certainly the warmer air in that case cannot possibly warm the lake.
      But if the water is cold enough and the humidity is high enough and the temperature difference is great enough, then certainly the air can warm the lake, but only up to a certain point at which the evaporation then prevents any further warming.

      Hopefully that is adequately simple and yet not too inaccurate. So the short answer is …

      “it all depends”

      • theyouk says:

        Thanks Neal. The interesting thing about part of your comment “if the water is cold enough and the humidity is high enough…[ ]..then certainly air can warm the lake..” wouldn’t it thus be the humidity doing the warming–which is essentially ‘warm water entering the system’? Have a great weekend all!

        • Neal S says:

          “It all depends”

        • Neal S says:

          I should add, that given a high enough temperature difference, then no matter what the humidity, the air should be able to warm the water up to a certain point. So in the case of zero humidity, hot enough air can still warm cool enough water, and it is NOT water doing the heating of the water.

  10. davidswuk says:

    Now we know why you still don`t……………..

  11. Edmonton Al says:

    OK Heat flows from warm to cold until the balance. [no additional heat source]
    I have a pot with 1 cup of water in it @40C. I have another cup of eater @20C.
    I pour the 20C cup into the 40C pot, stir and now have 2 cups @ 30C
    The hot heats up the cold until they are the same.

  12. nickreality65 says:

    I have no problem with the green house analogy. It’s imperfect, but I think it illustrates the point especially for the general public. Oddly enough I’m fond of my swimming pool analogy. If atmospheric temperatures increased by CO2 levels heat the ocean, how come 105 F temperatures don’t heat all those Phoenix swimming pools? Because evaporation cools those pools 55 times better than the air heats them.
    I run a gallon of water into a big pot and place it on the stove burner to boil for to cook some pasta. 8.33 pounds. Sea level, 14.7 psia.
    Increasing the water temperature from 60 F to 212 F takes sensible heat of 1 Btu/lb-F, 152 Btu, 44.5 watt hours. Once the water reaches 212 F it will begin to evaporate at that steady temperature and if boiled away will absorb about 8,330 Btu, 2,440 watt hours.
    Evaporating one pound of water from 60 F to 100% water vapor takes 2,484.5 watt hours, 1.8% in sensible heat, 98.2% in latent heat with no temperature change.
    I have two objects – in a closed system. Heat will flow from the hot object to the cold object. How fast depends on the medium, i.e air, water, vacuum, copper, etc. R=1/U, Resistance is the inverse of thermal conductivity. The hot object will get cooler and the cold object will get warmer. If I insert some kind of less than perfect insulation, the rate of energy transfer (due to thermal conductivity) will slow, but not stop. The hot object will still get colder and the cold object will get warmer.
    An open system has two objects, one hot & one cold, at equilibrium with 3,412 Btu/h (1 kW) flowing from hot to cold. If I insert an insulator between the two objects the heat flow is reduced, we’ll say to 1,706 Btu/h (.5 kW). The two objects remain at the original temperatures, but the heat flow slows down.
    If the heat transfer slows, does the hot object simply cool more slowly or actually get hotter? I suggest that it doesn’t get hotter unless you up the input.
    If I want to maintain the original 3,412 Btu/h (1 kW) the hot object will have to get hotter, maybe by feeding 2 kW.
    My BSME suggests I should know a little about heat transfer, too.

  13. As written what Steve gives is a universe with only two objects: one at a higher temperature to the other.

    As such, there is only one thing which can happen which is that heat flows from the warmer object to the colder and the warmer object will cool and the cooler object will warm until they are both at the same temperature.

  14. nickreality65 says:

    Well, thanks. Rather “unsettling” wouldn’t you say?

  15. nickreality65 says:

    “All other things being equal, the warmer the water, the greater the evaporation rate.”

    It’s the relative concentrations that drive evaporation, not the temperatures. Granted, warm air will absorb more water, I’m not sure about the rate.

    If air has to absorb X Btu/hr, it’s flow rate becomes an issue. Btu/lb * Lb/h.

  16. A convection system not a greenhouse. Good now we are getting the right framework in place.

  17. Tim says:

    I just put outside a cup that’s wrapped as if wearing a jacket and filled with chocolate milk the temps about 26° f., when do you think my hot cocoa should be ready?

  18. nickreality65 says:

    Several decades ago, early sixties, my cousins and I were stacking hay bales at my grandfather’s farm outside Las Animas, CO. As it was a hot summer’s day we had brought along one of those canvas covered water bags. For those who haven’t seen one, there’s a picture on one of Jackson Browne’s albums. Before you filled the bag you had to saturate the canvas with water. The water would evaporate and cool the contents, water, wine, beer. The evaporating water would approach the wet bulb temperature determined by the ambient humidity, maybe 10 or 15 F below the ambient dry bulb. (90 F, 30% – 67 F WBT) One of my cousins dropped the bag from several rows up. Don’t do that. Split that bag wide open. No forgiveness in incompressible water.

    I think this is what Miatello means by a refrigerator rather than a blanket or greenhouse. The water cycle cools the earth. In a refrigeration cycle the ammonia or Freon is compressed and when it expands its temperature drops. The water cycle absorbs energy and cools when it releases that heat through evaporation w/o a sensible temperature increase, only an increase in RH.

    My only objection to Miatello’s paper is his suggestion that entropy has something to do with randomness. Not so. Entropy is about heat & energy. Order/disorder, random/not random have exactly zero to do with it.

    Entropy says that a closed system will degrade from a higher energy level to lower energy level. If I had to bring random/order into it I would say from a high energy/highly disordered/random state to a low energy/less disordered/random state. Pretty much the opposite of the creation science interpretation. Greater order and lower energy are entropy’s natural flow.

    • Curt says:

      Nick: It’s hard to get thermodynamics more wrong that you have in this comment. Please take some kind of formal course in thermodynamics before you make a bigger fool of yourself.

      You say, “My only objection to Miatello’s paper is his suggestion that entropy has something to do with randomness. Not so.”

      Nick — Entropy, BY DEFINITION, is a measure of randomness. The higher the entropy, the higher the randomness. This is very basic, introductory stuff.

      You say, “Entropy says that a closed system will degrade from a higher energy level to lower energy level.” HOGWASH! (And you know what I wanted to say…) A closed (technically, isolated) thermodynamic system BY DEFINITION has constant energy.

      You say, “If I had to bring random/order into it I would say from a high energy/highly disordered/random state to a low energy/less disordered/random state.” Exactly backwards!!! Isolated systems evolve toward maximum randomness/disorder. If they start out with temperature differences, these will disappear. If they start out with pressure differences (other than in a constant gravitational field), these will disappear.

      And you miss the glaring errors right from the beginning of Miatello’s paper…

  19. Baa Humbug says:

    Here are the rules :

    1 – Heat flows from warmer objects to cooler objects
    2 – Heat can not flow from a cooler object to a warmer object

    Therefore, if the temperature of the cooler object increases – the only way to maintain the condition of rule 1 is for the temperature of warmer object to also increase.

    Should the above not read….”Therefore, if the temperature of the cooler object increases to be higher than the source – the only way etc”

    • Andrew S says:

      “if the temperature of the cooler object increases to be higher than the source”, then call your local fire department!

    • No. In order to continue removing all of the heat from the constant heat source, the temperature differential between the two points has to remain the same.

      • Baa Humbug says:

        No. In order to continue removing all of the heat from the constant heat source, the temperature differential between the two points has to remain the same.

        There was no mention of “removing all of the heat”, only the condition under which rule one applies.
        Heat will flow from source to the cooler object so long as the differential exists. Once the differential is zero, the source and ‘cooler’ object are the same temperature, heat flow stops.

        e.g. Lounge room at ambient 19C and the usual furniture also at 19C (ambient see).
        If a cold new piece of furniture is placed in the room, it will eventually reach ambient T BUT IT WILL NEVER EVER EVER RAISE THE TEMPERATURE OF THE ROOM OR ANY OTHER PIECE OF FURNITURE.

        If I’m wrong, please explain so I can wise up.

        • Curt says:

          Baa: One key thing that you are missing is that ambient for earth — that is, the temperature of earth’s surroundings — is -270C (3K). The earth is constantly shedding heat to this ambient, and on average, it must transfer as much heat to this very cold deep space as it receives from the sun. So if the surface can transfer heat instead to the upper atmosphere at about -20C (253K) instead of -270C, it needs to have a higher temperature to provide as much heat loss as if it were radiating directly to space.

          So your analogy isn’t really appropriate. In a better analogy, you would have a space heater in this room and thin walls on a cold winter day. With the thin walls, the heater is not keeping the room warm enough. I propose to add insulation to the inside of the walls so the room can be warmer. Someone else says, “No, the insulation, being between the room and the cold outside, will have a lower temperature than the room. So it cannot possibly increase the temperature of the room further.”

          Who’s right?

        • Baa Humbug says:

          @curt
          The post is about objects. It is about cooler objects making warmer objects warmer still.
          I gave an example of a cooler object (lounge chair) being placed in a room with warmer objects (other lounge chairs), so I’m not missing anything.

          The only confusion as far as I can see is that the post talks about heat flow, but in subsequent comments there’s talk about “removing all of the heat”.
          Maybe I misunderstood but that hasn’t been made clear to me.

        • Curt says:

          Baa:

          I gave an example of a colder object (wall insulation) making warmer objects (like lounge chairs in a room) warmer still. There are two aspects to my analogy, but both totally relevant to the earth’s system;

          1. Separate energy source: space heater, sun

          2. Cold ambient: outside on a winter day, deep space

      • Baa Humbug says:

        OK we really need to tidy all this up before it gets embarrasing.

        A room at ambient temperature. It has 3 lounge chairs in it.
        Everything in the room will eventually be at the same temperature because given a constant heat source, eventually each chair will radiate as much as it receives and voila’ we’re in equilibrium.
        CAN WE AGREE SO FAR?

        In caricature think of 3 jugglers throwing tennis balls between each other. At EQUILIBRIUM say each juggler has 2 balls in their hand at any given time.

        Now we bring into the lounge room a fourth chair which is much cooler than the ambient.
        The first thing that will happen is that the temperature of the room will drop. How much doesn’t matter, it will always drop.
        Until such time as the fourth lounge reaches ambient temperature, the room will be COOLER than it otherwise was. BUT IT WILL NEVER BE WARMER THAN IT ORIGINALLY WAS JUST BECAUSE AN EXTRA CHAIR WAS ADDED.

        Back to the caricature. A fourth juggler joins in with empty hands. For a period, only 6 balls will pass between four jugglers, then 7 balls then 8 balls AT WHICH TIME THEY ARE IN EQUILIBRIUM. Two balls per juggler.

        If matter didn’t emit as well as it absorbs or conversely didn’t absorb as well as it emits, we’d have to rewrite physical laws.

        Kirchoff: the essential point is that if we suppose a particular body can absorb better than it emits, then in a room full of objects all at the same temperature, it will absorb radiation from the other bodies better than it radiates energy back to them. This means it will get hotter, and the rest of the room will grow colder, contradicting the second law of thermodynamics. (We could use such a body to construct a heat engine extracting work as the room grows colder and colder!)
        [ I bolded the above para because I cut n pasted it off of a science site]

      • nickreality65 says:

        The insulator will restrict the heat flow, so to maintain the original heat flow the differential must get larger, i.e. the hot source must get hotter. (or cold colder)

  20. gymnosperm says:

    About that Water vapor and CO2 coat, what was I thinking? I don’t need to make it, you already have it, the very same one the planet has. All you need to do is walk outside naked to see how well it works. Granted at 273 +37=310K @ 100 watts you are running hotter but a lot dimmer than 255K @ 174 PW earth spectrum but not that much hotter…

  21. Andrew S says:

    Wow. I don’t think Tony(Steven) is a masochist, but he’s sure coming up with some interesting responses here to his Heat Flow Proof (for Dummies).

    I (the warmer object [98.6 F]{source}) returned home this evening to my 63 F degree home(cooler object{sink}). After about an hour or two of perusing Al Gore’s internet, I began to feel a chill set in to my bones so I turned up the thermostat to 65 F. Now I don’t feel so bad. It will take a few more cycles of the furnace, and maybe half of this night to re-stabilize the ambient heat of the house to where it is fully comfortable once again. Now as the furnace cycles the thermostat is bouncing between 64 F and 68 F, (it’s mounted on an interior wall); and the thermometer of my atomic clock (mounted on the inside of an exterior wall-window frame to be exact-) is bouncing from 61.5 F to 62.2 F.
    All of the following apply:
    1 – Heat flows from warmer objects to cooler objects
    2 – Heat can not flow from a cooler object to a warmer object

    Therefore, if the temperature of the cooler object increases – the only way to maintain the condition of rule 1 is for the temperature of warmer object to also increase.

    There’s one exception to Rule 2. : Refrigerators use heat pumps to move heat from the inside of a cold refrigerator(source) to the room temperature air of the kitchen(heat sink). but really it’s no exception because it takes heat energy to do it. In one case the heat pump is a “heater”, and in the other case the heat pump is a “refrigerator.” Alternatively I could put my window unit Air conditioner in backwards but I think that would be a waste of electricity, Natural gas is so much more efficient!

  22. Eliza says:

    SG You certainly are getting more comments from a non-issue LOL. ie “They” seem to be flogging a dead horse…hahaha.

  23. davidswuk says:

    Heat Pumps (refrigerators) have a CoP of about 3:1 and so, depending upon your gas/electric tariffs, (about 7p/15p/kWhr here), it might make sense to punch a few big holes through an outside wall and fill them with back-to-front `fridges with doors removed of course. But you wouldn`t have much of a house left if you didn`t fit big circulating fans in them there `fridges to provide them with sufficient ambient air from which to suck some useful heat – unless that is you live in “Phoney-Tony” Land where heat comes for free.

  24. nickreality65 says:

    Ok, I screwed up my example. To maintain the original set point temperature of the hot object with the added insulation would require half the heat input, .5 kW. Without a thermostat to reduce the heat input of 1 kW, the hot object is going to get hotter. Without a thermostat…… (a straw man conditional, btw)

    The house thermostat is set at 65 F, it’s 30 F outside. I do all those activities to cut my energy loss in half. To maintain the 65 F set point the furnace now has to deliver half as much heat. If the furnace continues to fire at the same rate w/o the thermostat, the house would get really hot.

    I’m outside in my shirt sleeves. It’s 30 F. I’m losing heat and getting cold. I wrap a blanket around my body & get warmer. And a second. And a Mylar survival blanket. And a $350 Hudson Bay 100% wool, cream colored with red and yellow stripes. And guess what? I start to overheat so my body’s thermostat turns on the water vapor cooling/refrigerator – I begin to sweat.

    Let’s stick with the green house analogy. I’m going to hazard a guess that as the day warms up and sunlight streams into a greenhouse the relative humidity increases as the water vapor cooling/refrigerator thermostat operates. As the day cools, clouds appear, overnight, the relative humidity fluctuates.

    The earth’s atmosphere has a climate thermostat called (Miatello’s) water vapor cooling/refrigeration cycle.

    CO2/GHGs aren’t even significant players.

    So, kiddoes, here’s your science fair project. Two identical glass or Plexiglas boxes, maybe 3’ cubes. One is empty, the other has a pan of water in it. Set them outside in the sun. Track the internal temperatures and relative humidity. The hypothesis is that the empty box is going to get really, really hot while the box with the pan of water will stay much cooler as the relative humidity increases, the water vapor cooling/refrigerator thermostat at work. Maybe as an option fill them with 200, 300, 400, 800, 1,000,000 ppm CO2.

  25. Mr Pettersen says:

    This challenge are based on false logic. The hotter objekt does not need to be hotter also. If the coldest object gets varmer the objects may have the same temperature or the previus hottest object simply end up as the coldest and heat flow is reversed!

    It all depends on how the extra heat is delivered to the system. If you electrically heat the coldest object you will end up with a different result than if you heat both objects or the whole volume they both are located in.

  26. nickreality65 says:

    The problem with the GHE as used by AGW/CCC advocates and even Steve is that it is a dry greenhouse, without water vapor, considering only the LWIR, SWIR, jumping electrons and sensible heat. A greenhouse made of straw.

    The real greenhouse, made out of brick, with water vapor, modulates the internal temperature using Miatello’s water evaporation/condensation cooling/refrigerator thermostat.

    It’s a matter of simple observation, doesn’t even need differential calculus.

  27. Centinel2012 says:

    Reblogged this on Centinel2012 and commented:
    Now if only Hansen and the IPCC understood this.

  28. John Larson says:

    Let’s assume that there is no water vapor or clouds in the atmosphere and there is no convection – the sun heats up the earth’s surface during the day and the atmospheric gases also adsorb some heat. When the sun goes down – isn’t the earth’s surface warmer than the gases in the atmosphere? I know there is a rule of thumb that it is 2 degrees C cooler for every 1000 feet of altitude. How could there be any heat flow from the gases back to the surface when heat flows from the warmer object towards the cooler object? Any CO2 in the atmosphere (with no convection) must be cooler than the surface and radiate only to the colder outer space.
    jochlarson

  29. Timo Soren says:

    Steve finally fesses up and explains that his statement of ‘maintain’ is that a.) the amount of heat flow must be held constant, (because I can allow it to drop to a lower rate by not adding energy but still having a positive gradient) and that the maintainence period must be infinity, (not 1000 years, not 1,000,000 years but infinity). Because otherwise: one solution that violates his statement is: Place two object at a differential of, say 1000 degrees, allow the cooler object to gain from radiation and allow the warmer object to cool, the heat flow continues as a positive towards the cooler object but has not decreased to zero. After a period of cool though, to prevent equilibrium we must add energy to the warmer source and increase it’s temp. So I specifically take issue with combination of condition one: heat flows and Steve’ use of maintaining condition one. The fact that I can have the warmer object cool then increase can be argued that the warmer MUST increase is satisfied. Then however, I can allow the cooler object to decrease then increase and repeat and never have the warmer object increase. So clarity is a must!

  30. Bob Knows says:

    Does heat flow? The first problem with your contention that heat flows from warmer to cooler is that heat doesn’t really flow at all. Water, gas, and electrons can flow, but heat? Probably not without outstretching the meaning of “flow.” Heat transfer may be visualized by an analogy with flow, but heat doesn’t really flow. Heat is actually a measurement of the energy state of the particles in a material. Materials can lose energy by radiation, or by being in contact with material having less energy. Hot air can flow, and hot iron can flow, but the heat will only dissipate through the material or into the next material. A small amount of heat will leave the surface by radiation. Most heat transfer, including many of the above cited examples, are by convection or physical relocation of the material which has a high energy state.

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