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Thread: Heat Pump Question

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    Heat Pump Question

    We are going to have to replace gas boilers with electric heat pumps for domestic heating and hot water.

    Why do heat pumps use a refrigerant?

    It seems to me, all that is needed is a compressor to compress air. Pipe in air from outside, compress it in a heat exchanger inside the building, use its increased temperature to heat water or room air, then release it back outside through a valve.
    After all, adiabatic compression, in theory, raises the temperature of air by 453K with a compression ratio of only 10:1.

    https://en.wikipedia.org/wiki/Adiabatic_process

    Also, if I wish to vary the temperature, adjusting the outlet valve to higher or lower pressure will give a near instantaneous response.

    I am thinking some forum members with a better understanding of thermodynamics than I will tell me what is wrong with this idea.

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    Quote Originally Posted by kzb View Post
    We are going to have to replace gas boilers with electric heat pumps for domestic heating and hot water.

    Why do heat pumps use a refrigerant?
    Because the point is to pump heat efficiently up a thermal incline. Sure, there are other ways to heat a house with electricity, like resistance heating, but at most you can convert 100% of the electricity to heat that way. Given that the typical fossil fuel power plant is around 30-40% efficient, unless your electricity comes from hydro, solar, wind or nuclear you would be better with a high efficiency gas heater (somewhere in the mid 80s to 90+ percent efficient) in terms of efficient fuel use.

    But heat pumps don’t make heat, they move heat that already exists up the thermal hill. Using the same amount of electricity they can warm a house substantially more than 100% efficient resistance heating.

    But heat pumps have their own issues. The colder it is outside, the more energy it takes to pump the heat up the incline, and it will take longer to heat a house as well. In colder climates it didn’t used to make sense to use a heat pump for heating, and nobody would willingly switch from a good gas heating system. But newer high efficiency designs allow practical use in climates where they didn’t previously make sense.

    The upshot: If you want heat using electricity, pumping it is better than making it (until it gets too cold), and if you are pumping it, you want the highest practical efficiency.

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    Quote Originally Posted by kzb View Post
    Why do heat pumps use a refrigerant?
    Air doesn't give you much bang for your buck. A denser fluid works better because it holds more heat.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by Noclevername View Post
    Air doesn't give you much bang for your buck. A denser fluid works better because it holds more heat.
    I think they were thinking of something different. They weren’t talking about transporting heat by air, but rather of heating through compression rather than by transporting heat.
    As above, so below

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    Quote Originally Posted by Jens View Post
    I think they were thinking of something different. They weren’t talking about transporting heat by air, but rather of heating through compression rather than by transporting heat.
    I was specifically addressing the issue of refrigerant.
    "I'm planning to live forever. So far, that's working perfectly." Steven Wright

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    Quote Originally Posted by kzb View Post
    We are going to have to replace gas boilers with electric heat pumps for domestic heating and hot water.

    Why do heat pumps use a refrigerant?

    It seems to me, all that is needed is a compressor to compress air. Pipe in air from outside, compress it in a heat exchanger inside the building, use its increased temperature to heat water or room air, then release it back outside through a valve.
    After all, adiabatic compression, in theory, raises the temperature of air by 453K with a compression ratio of only 10:1.

    https://en.wikipedia.org/wiki/Adiabatic_process

    Also, if I wish to vary the temperature, adjusting the outlet valve to higher or lower pressure will give a near instantaneous response.

    I am thinking some forum members with a better understanding of thermodynamics than I will tell me what is wrong with this idea.
    The key physical property is latent heat of evaporation. By compressing a vapour to a liquid you release heat and by letting it evaporate again you suck heat in. That works with water, ammonia, freons various , ether, etc. Depending on details.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by Van Rijn View Post
    Because the point is to pump heat efficiently up a thermal incline. Sure, there are other ways to heat a house with electricity, like resistance heating, but at most you can convert 100% of the electricity to heat that way. Given that the typical fossil fuel power plant is around 30-40% efficient, unless your electricity comes from hydro, solar, wind or nuclear you would be better with a high efficiency gas heater (somewhere in the mid 80s to 90+ percent efficient) in terms of efficient fuel use.

    But heat pumps don’t make heat, they move heat that already exists up the thermal hill. Using the same amount of electricity they can warm a house substantially more than 100% efficient resistance heating.

    But heat pumps have their own issues. The colder it is outside, the more energy it takes to pump the heat up the incline, and it will take longer to heat a house as well. In colder climates it didn’t used to make sense to use a heat pump for heating, and nobody would willingly switch from a good gas heating system. But newer high efficiency designs allow practical use in climates where they didn’t previously make sense.

    The upshot: If you want heat using electricity, pumping it is better than making it (until it gets too cold), and if you are pumping it, you want the highest practical efficiency.
    I know this already, but I doubt the government does.

    Personally I think depending on a heat pump is nuts in a climate like the UK. We just had the coldest January in at least ten years, with sub 5 degree temperatures (C) day after day. You only have to look at online forums to see what a miserable and expensive time the heat pumpers had.

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    Quote Originally Posted by profloater View Post
    The key physical property is latent heat of evaporation. By compressing a vapour to a liquid you release heat and by letting it evaporate again you suck heat in. That works with water, ammonia, freons various , ether, etc. Depending on details.
    Yes that is how they work. But I am asking why not simplify the process. I appreciate the pressure to be withstood will be lower with a refrigerant, but is that the only reason?

    I was worried people would say there is no point because you are only going to get the same heat output as the work done by the compressor. But I don't think that is correct because the exhausted air will cool as it exits the valve to the outside, to a temperature lower than it had before compression. So heat has been extracted from the air.

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    Quote Originally Posted by profloater View Post
    The key physical property is latent heat of evaporation. By compressing a vapour to a liquid you release heat and by letting it evaporate again you suck heat in. That works with water, ammonia, freons various , ether, etc. Depending on details.
    Let me describe what I propose a little better:

    inside the home I have a compressor. It takes air from outside and compresses it inside the home, contained in a heat exchanger (I'm not proposing pressurising the whole house !).

    For arguments sake let's say the compression ratio is 10:1. What will happen is the compressed air temperature will increase by 453 K and the pressure will increase by a factor of 25 (not 10, because the temperature increases).

    The compressed air is then cooled to the ambient temperature of the house interior, which will be say 10 to 30K higher than outside. The pressure will be a bit higher than 10 atmospheres but a lot lower than 25 atmospheres.

    It is then piped back outside the house and released through a pressure valve. As it undergoes adiabatic expansion outside the house it will cool to a temperature lower than the ambient outside temperature. Which means heat has been extracted from it, and the heating efficiency of my compressor is more than 100% (relative to the electricity input).

    Is there anything wrong with this and isn't it simple?

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    Quote Originally Posted by profloater View Post
    The key physical property is latent heat of evaporation. By compressing a vapour to a liquid you release heat and by letting it evaporate again you suck heat in. That works with water, ammonia, freons various , ether, etc. Depending on details.
    Let me describe what I propose a little better:

    inside the home I have a compressor. It takes air from outside and compresses it inside the home, contained in a heat exchanger (I'm not proposing pressurising the whole house !).

    For arguments sake let's say the compression ratio is 10:1. What will happen is the compressed air temperature will increase by 453 K and the pressure will increase by a factor of 25 (not 10, because the temperature increases).

    The compressed air is then cooled to the ambient temperature of the house interior, which will be say 10 to 30K higher than outside. The pressure will be a bit higher than 10 atmospheres but a lot lower than 25 atmospheres.

    It is then piped back outside the house and released through a pressure valve. As it undergoes adiabatic expansion outside the house it will cool to a temperature lower than the ambient outside temperature. Which means heat has been extracted from it, and the heating efficiency of my compressor is more than 100% (relative to the electricity input).

    Is there anything wrong with this and isn't it simple?

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    Quote Originally Posted by kzb View Post
    Yes that is how they work. But I am asking why not simplify the process. I appreciate the pressure to be withstood will be lower with a refrigerant, but is that the only reason?

    I was worried people would say there is no point because you are only going to get the same heat output as the work done by the compressor. But I don't think that is correct because the exhausted air will cool as it exits the valve to the outside, to a temperature lower than it had before compression. So heat has been extracted from the air.
    Without the latent heat, you do work compressing the gas and then you release it through an engine, preferably, getting out work and heat. But you lose the heat , which is less than the heat equivalent of the work you put in. With high pressure air you also get freezing as the pressure releases, from a cold cylinder, but you let all that initial heat leak away, so not adiabatic. So the good old second law is against you. By doing the work, you get heat , if you can release that heat to the outside environment, you can use the not so pressurised air to cause cooling as it expands, but it is less than the work you put in. With latent heat you get the heat pump effect so that the heat goes in at the lower temperature, with some work, and is released at a higher temperature, plus a lesser work. The heat pumped can be, say, four times the work needed.

    In leaves, the evaporation of water takes heat from both air and leaf, causing a suction which can do work raising the water from the ground. No moving parts! Without latent heat exchange, that would be impossible.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by kzb View Post
    Let me describe what I propose a little better:

    inside the home I have a compressor. It takes air from outside and compresses it inside the home, contained in a heat exchanger (I'm not proposing pressurising the whole house !).

    For arguments sake let's say the compression ratio is 10:1. What will happen is the compressed air temperature will increase by 453 K and the pressure will increase by a factor of 25 (not 10, because the temperature increases).

    The compressed air is then cooled to the ambient temperature of the house interior, which will be say 10 to 30K higher than outside. The pressure will be a bit higher than 10 atmospheres but a lot lower than 25 atmospheres.

    It is then piped back outside the house and released through a pressure valve. As it undergoes adiabatic expansion outside the house it will cool to a temperature lower than the ambient outside temperature. Which means heat has been extracted from it, and the heating efficiency of my compressor is more than 100% (relative to the electricity input).

    Is there anything wrong with this and isn't it simple?
    You say you compress the air inside the house then release the heat, what, inside the house? So you heated the house with work. Then you release the air now cooled outside to cool the outside?

    As a cooling method you can pressurise air outside, and let it cool, outside, then bring the cylinder in and release it getting cooling. But that is not a heat pump. As before you get less cooling than the work done.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by kzb View Post
    Let me describe what I propose a little better:

    inside the home I have a compressor. It takes air from outside and compresses it inside the home, contained in a heat exchanger (I'm not proposing pressurising the whole house !).

    For arguments sake let's say the compression ratio is 10:1. What will happen is the compressed air temperature will increase by 453 K and the pressure will increase by a factor of 25 (not 10, because the temperature increases).

    The compressed air is then cooled to the ambient temperature of the house interior, which will be say 10 to 30K higher than outside. The pressure will be a bit higher than 10 atmospheres but a lot lower than 25 atmospheres.

    It is then piped back outside the house and released through a pressure valve. As it undergoes adiabatic expansion outside the house it will cool to a temperature lower than the ambient outside temperature. Which means heat has been extracted from it, and the heating efficiency of my compressor is more than 100% (relative to the electricity input).

    Is there anything wrong with this and isn't it simple?
    I’m sorry I slanted my replies toward cooling, but of course heat pumps can and do work both ways. So you can use a compressor as a heater, you can turn work into heat, but it would be better to use the same electricity in a resistor at 100%. The joy of heat pumps is that thanks to latent heat, you can get more heat than the work done. The extra heat is taken through the wall barrier from a heat source you get for free. So that heat is not converted to work. The second law , or Carnot, says you cannot turn heat to work without rejecting heat at a lower temperature than it started out. The Carnot limit.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    I’m sorry I slanted my replies toward cooling, but of course heat pumps can and do work both ways. So you can use a compressor as a heater, you can turn work into heat, but it would be better to use the same electricity in a resistor at 100%. The joy of heat pumps is that thanks to latent heat, you can get more heat than the work done. The extra heat is taken through the wall barrier from a heat source you get for free. So that heat is not converted to work. The second law , or Carnot, says you cannot turn heat to work without rejecting heat at a lower temperature than it started out. The Carnot limit.
    The air is released to the outside at a lower temperature than it entered the compressor, after providing more heat to the house than a 100% efficient resistive heater. It's a heat pump, it just uses ambient working fluid instead of an enclosed loop.

    The problem is the amount of air you'll need to compress to get effective heating/cooling. A little tube carrying hot compressed air is not a very effective way to move heat. Useful working fluids have higher heat capacities and typically use phase changes to move even more heat. Air can technically work, but will require bigger, louder compressors, larger tubes, etc.

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    Quote Originally Posted by cjameshuff View Post
    The air is released to the outside at a lower temperature than it entered the compressor, after providing more heat to the house than a 100% efficient resistive heater. It's a heat pump, it just uses ambient working fluid instead of an enclosed loop.

    The problem is the amount of air you'll need to compress to get effective heating/cooling. A little tube carrying hot compressed air is not a very effective way to move heat. Useful working fluids have higher heat capacities and typically use phase changes to move even more heat. Air can technically work, but will require bigger, louder compressors, larger tubes, etc.
    Finally someone who gets it !

    Compressing air makes it easy to vary the temperature by adjusting the pressure. Plus the temperature available is a lot higher, a 453K increase for 10:1 compression. Current heat pumps heat water to about 30-40 degrees and you need to install bigger radiators.

    However there must be a catch to it. What I am not capable of doing is calculating the thermodynamic efficiency, although I realise the efficiency will fall as the temperature difference between inside and outside increases.

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    Quote Originally Posted by cjameshuff View Post
    ... The problem is the amount of air you'll need to compress to get effective heating/cooling. A little tube carrying hot compressed air is not a very effective way to move heat. Useful working fluids have higher heat capacities and typically use phase changes to move even more heat. Air can technically work, but will require bigger, louder compressors, larger tubes, etc.
    So an ideal medium is a fluid with high latent heat of vaporization, whose phase change occurs at temperature that is not extreme, and with a high specific heat capacity?

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    The Youtuber "Technology Connections" did an extensive video about heat pumps about a month ago. He explains the whole thing really well, including the whole latent heat principle. Plus, he's entertaining.

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    Quote Originally Posted by kpatz View Post
    The Youtuber "Technology Connections" did an extensive video about heat pumps about a month ago. He explains the whole thing really well, including the whole latent heat principle. Plus, he's entertaining.
    Thanks I will try and find that later.

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    Quote Originally Posted by cjameshuff View Post
    The air is released to the outside at a lower temperature than it entered the compressor, after providing more heat to the house than a 100% efficient resistive heater. It's a heat pump, it just uses ambient working fluid instead of an enclosed loop.

    The problem is the amount of air you'll need to compress to get effective heating/cooling. A little tube carrying hot compressed air is not a very effective way to move heat. Useful working fluids have higher heat capacities and typically use phase changes to move even more heat. Air can technically work, but will require bigger, louder compressors, larger tubes, etc.
    No it is not a heat pump. In closed room A you compress air into a cylinder. The remaining air in A is cooled by the reduction of pressure. The cylinder now has some of your work converted as heat and some as pressure. You let the heat back into A. Obviously less than 100% of the work equivalent. You go to closed room B and release the pressure, cooling the air in the cylinder by reducing pressure but also heating the room B air by increasing its pressure. In the end the net heat effect is the work you put in. You have a heater in A but not a heat pump. To be a heat pump you must extract heat at a lower temperature and deliver it at a higher temperature. In the scheme a resistor would be 100% effective but the pressure taken outside to be vented is just a loss. So the heater is less than 100% effective.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    No it is not a heat pump. In closed room A you compress air into a cylinder. The remaining air in A is cooled by the reduction of pressure. The cylinder now has some of your work converted as heat and some as pressure. You let the heat back into A. Obviously less than 100% of the work equivalent. You go to closed room B and release the pressure, cooling the air in the cylinder by reducing pressure but also heating the room B air by increasing its pressure. In the end the net heat effect is the work you put in. You have a heater in A but not a heat pump. To be a heat pump you must extract heat at a lower temperature and deliver it at a higher temperature. In the scheme a resistor would be 100% effective but the pressure taken outside to be vented is just a loss. So the heater is less than 100% effective.
    Buildings don't work that way. Nor does the system kzb described.

    You compress outside air. In doing so, you heat it above the desired indoor temperature, and run it through a heat exchanger to cool it and heat the building. You then vent it through an expanding valve back to the outside, at lower temperature than it started, having heated the building with all the work you put into it and with the heat you've extracted from it, making it more efficient than a resistive heater. It's plainly a heat pump. It will function as described, it just won't provide much heating value for a given compressor and heat exchanger size.

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    Quote Originally Posted by cjameshuff View Post
    You then vent it through an expanding valve back to the outside, at lower temperature than it started, having heated the building with all the work you put into it and with the heat you've extracted from it, making it more efficient than a resistive heater. It's plainly a heat pump.
    But how much more efficient? I would expect you would get so little advantage over a resistive heater that you might as well use a resistive heater even with a mild climate.

    It will function as described, it just won't provide much heating value for a given compressor and heat exchanger size.
    So it isn’t a practical heat pump. If you actually try to use it as a heat pump, big enough to do something noticeable, given the energy needed to run the huge compressor, it would probably do worse than resistive heating. At minimum, the compressor should be inside the house so some of the heat produced from running it could be captured instead of wasted outside.

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    Quote Originally Posted by cjameshuff View Post
    Buildings don't work that way. Nor does the system kzb described.

    You compress outside air. In doing so, you heat it above the desired indoor temperature, and run it through a heat exchanger to cool it and heat the building. You then vent it through an expanding valve back to the outside, at lower temperature than it started, having heated the building with all the work you put into it and with the heat you've extracted from it, making it more efficient than a resistive heater. It's plainly a heat pump. It will function as described, it just won't provide much heating value for a given compressor and heat exchanger size.
    Agreed , the normal plan is to take outside cold air, so you compress it, getting heated air and pressure. You release the heat inside the house, but you release the pressure , after extracting the heat, outside again. The useful heat inside is less than the work done. The stored air is thus cooled and no use to the house. Although you could get some work back with a turbine. So the scheme is a heater but its COP is less than 1. To be a useful heat pump, worthy of the name, the COP must be more than 1. If the circuit is closed, the cold released air can be heated outdoors and recycled, this pushes the COP close to 1.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by Van Rijn View Post
    So it isn’t a practical heat pump. If you actually try to use it as a heat pump, big enough to do something noticeable, given the energy needed to run the huge compressor, it would probably do worse than resistive heating. At minimum, the compressor should be inside the house so some of the heat produced from running it could be captured instead of wasted outside.
    I assumed that was a given, considering we're specifically considering a heat pump built to heat a building.

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    Quote Originally Posted by profloater View Post
    Agreed , the normal plan is to take outside cold air, so you compress it, getting heated air and pressure. You release the heat inside the house, but you release the pressure , after extracting the heat, outside again. The useful heat inside is less than the work done. The stored air is thus cooled and no use to the house. Although you could get some work back with a turbine. So the scheme is a heater but its COP is less than 1. To be a useful heat pump, worthy of the name, the COP must be more than 1. If the circuit is closed, the cold released air can be heated outdoors and recycled, this pushes the COP close to 1.
    The air isn't stored anywhere. Releasing the air outside and compressing outside air is identical to having an infinitely effective heat exchanger warming air in a closed loop with outside air. COP is trivially going to be larger than 1, the problem is the scale of the entire system required to move a given amount of heat.

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    Quote Originally Posted by cjameshuff View Post
    The air isn't stored anywhere. Releasing the air outside and compressing outside air is identical to having an infinitely effective heat exchanger warming air in a closed loop with outside air. COP is trivially going to be larger than 1, the problem is the scale of the entire system required to move a given amount of heat.
    OK the outside is an effective heat exchanger. The heat delivered is at a higher temperature, and is less than the work done. Some work is stored as pressure , taken outside at slightly higher than the inside temperature, and not used for work heat. So the exhaust is at a higher T and P but could be cooled below the outside. If there are no other losses and you install a turbine to recover that pressure energy to aid the compressor perhaps, it could be called a heat pump. I think the real efficiencies will keep the COP under 1.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    I take your point that the mass of gas has been delivered at a lower T so some heat must have been pumped. But the compressor puts all the work into heat and pressure, the work gets harder as you ask for more pressure, then you throw the pressure energy away. The work done will be higher than the heat pumped, unless you have full recovery of the pressure energy in the cycle.
    sicut vis videre esto
    When we realize that patterns don't exist in the universe, they are a template that we hold to the universe to make sense of it, it all makes a lot more sense.
    Originally Posted by Ken G

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    Quote Originally Posted by profloater View Post
    I take your point that the mass of gas has been delivered at a lower T so some heat must have been pumped. But the compressor puts all the work into heat and pressure, the work gets harder as you ask for more pressure, then you throw the pressure energy away. The work done will be higher than the heat pumped, unless you have full recovery of the pressure energy in the cycle.
    It's certainly an interesting question if mechanical energy could be recovered from the outside pressure release, to help run the compressor. But then I recall this is thermodynamics we are dealing with here and it likely is not that simple. It's all part of the same thermodynamic engine.

    If you go back and read what I actually wrote in Post #10 it might help. In previous posts, you seem to be arguing about things that are not even part of the question.

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    Quote Originally Posted by Van Rijn View Post
    But how much more efficient? I would expect you would get so little advantage over a resistive heater that you might as well use a resistive heater even with a mild climate.



    So it isn’t a practical heat pump. If you actually try to use it as a heat pump, big enough to do something noticeable, given the energy needed to run the huge compressor, it would probably do worse than resistive heating. At minimum, the compressor should be inside the house so some of the heat produced from running it could be captured instead of wasted outside.
    Well your first sentence is really one of the questions I am asking.

    Yes, it is a given that the waste heat from the compressor is used to heat the house, as in a normal heat pump.

    I said it was inside the house, to get the concept across, but technically it does not need to be. Rather noisy I expect. But it does need a way of transferring heat to the house heating system.

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    Quote Originally Posted by kzb View Post
    Well your first sentence is really one of the questions I am asking.
    Well, it’s answered now, right? What you proposed is extremely impractical. Resistive heat would be much better. And the very first thing I discussed in thread is that refrigerant is used because you need an efficient system, and even conventional heat pumps until fairly recently were notorious for only being useful for heating in fairly mild climates.

    Yes, it is a given that the waste heat from the compressor is used to heat the house, as in a normal heat pump.
    Really? I’ve always seen heat pumps and house air conditioners with an outdoor compressor unit. Granted, it’s been decades since I saw a heat pump, so they were old style, and were more or less just modified air conditioners, but more robust and with a reversing valve. (Very early heat pumps were *very* slightly modified air conditioners and had a habit of quickly dying. By the ‘80s they were much more reliable.)

    Anyway, if you put a heat pump in cooling mode, that’s just extra heat to get rid of. And you really want to get most of your heat from the heat pump, not the waste heat from running a huge compressor.

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  30. #30
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    Quote Originally Posted by kzb View Post
    It's certainly an interesting question if mechanical energy could be recovered from the outside pressure release, to help run the compressor. But then I recall this is thermodynamics we are dealing with here and it likely is not that simple. It's all part of the same thermodynamic engine.

    If you go back and read what I actually wrote in Post #10 it might help. In previous posts, you seem to be arguing about things that are not even part of the question.
    I apologise for not being specific to the OP question. In any large latent heat system the high pressure is not just vented, it is used for mechanical work directly or indirectly to assist the compresser. If you think about the final stage where pressure is vented, there is cooling but the energy stored as pressure should be doing heating work. When vented it is lost as eddies which end up as heat, mostly, at the lower temperature.

    I should have been clearer that for me, a heat pump must have a coefficient of performance over 1. Otherwise it is a poor heater since you could just heat a resistor.

    Yes, in your scheme you do take colder air, and release heat at higher temperature, as you would by burning fuel. But the work done in increasing pressure is actually likely to be greater than the heating effect, so it is not trivial to vent that pressure and waste that work.

    I should have made those points more clearly. I maintain that with other inefficiencies the scheme can never gat a COP over 1 until you employ the considerable help of latent heat. So it is not just scale.
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