When you need heat pumps the most, they pump heat the least.
This is according to an unbreakable law of physics that applies to the entire universe without exception, even black holes, and especially to heat pumps.
Heat pump promoters who claim otherwise must have defeated the second law of thermodynamics, which would theoretically also allow them to make time run backward.
In addition to denunciation by physics, the cost of operating heat pumps is often very high compared to natural gas-fired heating.
Heat pumps are often accurately described as an air conditioner in reverse. To understand how a heat pump works, it helps to know how an air conditioner works.
How an Air Conditioner Works
An air conditioner transports heat from inside a house to the outside in a continuous circuit using a chemical mixture called a refrigerant.
The refrigerant is piped into the house as a liquid under high pressure and at a temperature just above the outside air temperature. It expands into a gas across a valve that has a lower pressure on the other side and becomes very cold, about 4°C (39°F).
This part of the air-conditioning unit is called the evaporator because it causes the liquid refrigerant to evaporate into a gas. The cooling is a bit similar to when you let air out of a tire and the expanding escaping air feels cold. (If you want to know more details, look up the Ideal Gas Law.)
The pipe with cold gas-phase refrigerant is then passed in front of a fan inside the A/C unit (or furnace if it’s central A/C) to cool the room.
The second law of thermodynamics dictates that two bodies at different temperatures will equalize in temperature when brought into contact with each other.
How fast this equalization occurs is driven by the temperature difference between the two bodies: the bigger the temperature difference, the faster the heat exchange happens.
The pipe containing the refrigerant gets cold because it’s in contact with the cold refrigerant, and the air outside the pipe gets cold because it’s in contact with the cold pipe.
A fan speeds up the contact of the warm air in the room with the cold pipe and as the heat from the air is transferred to the refrigerant, the refrigerant gets warmer.
The low-pressure and now warm refrigerant is then piped outside the building to an electrically driven compressor, which reduces the gas in volume and increases its pressure.
The compressor puts energy into the gas causing it to heat up (the Ideal Gas Law again). The hot high-pressure gas is then cooled to near outside temperature by passing the pipe containing the gas for several loops in front of a fan that uses outside air to cool and condense the gas into a high-pressure liquid (which is why it’s called the condensing unit).
The high-pressure and near-outside-temperature liquid refrigerant is then piped inside the building and the whole circuit starts over again.
This circuit is called the Carnot Cycle after the French physicist Sadi Carnot who discovered it in 1824. It wasn’t until 1902 that American engineer Dave Carrier produced the first air conditioner.
How a Heat Pump Works
To convert an air conditioning unit into a heat pump, you place the evaporator (which attracts heat) outside of the house and the condenser (which expels heat) inside the house.
Furthermore, the heat pump refrigerant is chemically different so that it can be cooled in the evaporator to minus 25°C (minus 13°F). The refrigerant has to be colder than the outside temperature to absorb outside heat.
The two perceived advantages of a heat pump are:
- If the electrical energy to run the heat pump was produced without carbon dioxide (CO2) emissions, it’s considered a green heating source. But all electrical generation has some form of environmental impact, most likely out of mind at a remote site.
- Because it collects free heat from the outside and delivers it inside, the only cost to run a heat pump is the electrical energy for the compressor and fans. A heat pump is more energy efficient because it transfers existing heat, rather than creating new heat by the combustion of a fossil fuel or biomass.
But here is the catch: Energy efficiency is not the same as economic efficiency.
At an outside temperature of 10°C (50°F) for every unit of energy used to run the heat pump (purchased electricity), the heat pump can collect four units of energy from the outside (heat delivered into your home). At this outside temperature, the efficiency of the heat pump is 400%.
When the outside air temperature drops to minus 20°C (minus 4°F), the efficiency of the heat pump drops to 200%; one purchased unit of energy input delivers only two units of free heating energy.
This is a result of the ambient temperature (minus 20°C) approaching the refrigerant temperature (minus 25°C) and reducing the rate of heat exchange between the two. It’s the second law of thermodynamics at play. The smaller the temperature difference, the more slowly the heat exchange occurs.
A conventional natural gas furnace delivers only 0.9 units of heat energy for each unit of purchased energy, for an energy efficiency of 90%.
When Heat Pumps Suck
Where I am writing normally has temperatures colder than minus 20°C 20 days per year, and the retail cost of electricity is nine times more than natural gas on an energy equivalent basis.
With an outside temperature of 10°C, to heat a room to the same temperature a heat pump would use only 22.5% of the purchased energy of a natural gas furnace (22.5% = 90%/400%). But the total cost of that purchased energy would be twice as much (22.5% X 9 = 2).
Under mild weather conditions, the heat pump already has twice the operating expense as a natural gas furnace. Under common winter conditions of minus 20°C, the energy efficiency of the heat pump drops to 200%. It uses only 45% of the purchased energy, but that purchased electricity costs four times more than natural gas.
Your natural gas bill charges you by the gigajoule (GJ) and your power bill charges you by the kilowatt-hour (kWh). Currently where I live natural gas is $4.89/GJ, and electricity is $0.16/kWh. I have a 90% fuel-efficient natural gas furnace.
The following temperature scenarios provide a rough approximation of the difference in cost between running a furnace and running a heat pump where I live:
- The outside air temperature is 10°C or warmer—Divide the gas cost by 60 to get the kWh equivalent energy cost. If this number is smaller than the cost of electricity in kWh, then it is cheaper to operate a natural gas furnace than a heat pump. $4.89/GJ (gas) divided by 60 equals $0.08/kWh (electricity). In this scenario, heating my home with gas is half the cost of electricity needed to operate a heat pump ($0.08/$0.16).
- The outside air temperature is near minus 20°C—Divide the gas price in GJ ($4.89) by 120 to get the kWh equivalent cost ($0.04). My natural gas furnace cost is one-fourth of the cost of operating a heat pump.
- The outside air temperature is minus 25°C or colder—Most retail models of home-use heat pumps will probably not work at all because the refrigerant has to be colder than the outside temperature. Many heat pumps have a conventional electrical resistance heating element built in as a cold temperature backup. This is confirmation by the design engineers that they can not beat the second law of thermodynamics.
[Note to reader: One GJ of natural gas equals 278 kWh of electricity, and is roughly equivalent to one million British Thermal Units (BTUs).]
What Heat Pump Promoters Won’t Tell You
Granted, in moderate climates where winter home heating is more for comfort than survival, and especially where summer air conditioning is desirable, a heat pump that’s switchable to an air conditioner is probably worth looking into. They are more energy efficient, but there’s more to consider. For example:
- Compared to natural gas furnaces, heat pumps can have a much higher operating cost, which governments attempt to overcome by taxing fossil fuels and using those taxes to subsidize “green” electricity.
- Natural gas and other combustion furnaces provide instant heat and can warm up a cold house much faster than a heat pump can.
- In very cold weather heat pumps suck.
If heat pump promoters deny the above statements, they must be Oppenheimer-smart and have found a way around the universal second law of thermodynamics. Ask them if they are working on a time machine next.
Ron Barmby (www.ronaldbarmby.ca) is a Professional Engineer with a Master’s degree, whose 40+ year career in the energy sector has taken him to over 40 countries on five continents. His book, Sunlight on Climate Change: A Heretic’s Guide to Global Climate Hysteria (Amazon, Barnes & Noble), explains in layman’s terms the science of how natural and human-caused global warming work.
Top photo of a heat pump in Germany by alpha innotec on Unsplash
Permission to use this article or any portions on other sites is freely allowed, provided that any such use is accompanied by author attribution and link.
This empowers homeowners to choose the most suitable heating and cooling solutions for their specific circumstances, ultimately ensuring comfort and efficiency in their homes. Thank you for sharing such insightful information!
Tyrone; I’m glad this helped. I think it is important that a free marketplace allows home owners to make those decisions, and not government mandates or unreasonable interference in energy supply.
Take away heat sources for Ordinary Americans but as it is with the privileged few get all the heat they want and Biden the Blunder the head snake
I have been fooling around with heat pump for at least the last 20 years. Sometimes changing them just after one year. Not because they were defective, but because more efficient ones kept on coming. Now, there are heat pumps that are 100% efficient at -20e C and 80% at -30e C. A few years ago, we had a few days of those -30e C, I set the indoor thermostat to +30e C and it took less than 10 minutes to reach this set temperature, even though it was -30e C outside. My house was built in the 1960, so it is not up to actual isolation standard. One must understand that from (-30e C) to (+30e C) there is a 60e C difference. In the summer time that spread is way less than this. For example if it is +35e C outside and you want 20e C inside, that difference is much smaller: 15e C. For years, ‘expert’ were calculating the require quantity of btu in cooling mode only, that is because older technology were on/off compressor, and not the variable one which we have today. And if you were adding too much btu into your system, the coil could freeze during summer time, not so anymore because of those variable speed compressor. Keep in mind the 60e C difference during winter time if you intend to make use of your heat pump during those very cold days. The way to go is to increase the amount of BTU, up to 12,000 btu more. If 24,000 Btu is sufficient for summer, the best if to go for 36,000. It won’t have a dramatic effect on your electricity bill, because of those variable speed compressors. Instead of running at full speed, it may run at 50% speed. I have 3 heat pumps, two for the main floor and one for the basement. On the main floor only one is needed during summer time, and it gives me plenty of cold. I do not make use of the one in the basement at all during summer, as some of that cold air goes into the basement. The two on the main floor are high efficiency; 80% at -30e C. In the basement (a different brand) that efficiency drops dramatically during winter time (third one in 3 years as I was not satify), I may have (not sure) 100% efficiency at -15e C, but maybe 60% at – 30e C. When it gets below -30e C, (maximum 4 days each year) I shut the power off on that one, and start the electric baseboard. Our electricity price always stays the same, meaning that we get charge the same per KW independently of how many KW we use. It does not fluctuate like in many other places.
One of the thing which is ‘forgotten’ (intentionally or not) is the defrost cycle, which can vary quite considerably from one machine/brand/model to the other, especially if there is a snow or ice storm. I have had machine in the past which would go into defrost mode many times within a single hour, and as it gets colder those cycle were way longer, and so it would give me about 15minutes of ‘real’ heat for 45minutes of no heat every hour. Most people tends to forget about those defrost cycles, which in fact are very energy demanding, for the compressor has to go into full speed, plus there is an electric coil that helps in melting down that ice or snow build up on the outside unit; no saving here at all. The two units I have on the main floor in the worst possible condition; -20e C plus snow storm, still does a very good job, as they give me at least 3-6 hours of continuous heat and only a few minutes of defrost time. And as the snowstorm ends, so are the defrost cycle, maybe one (very short one) every 24-48 hours.
To conclude look for % of efficiency at -20e C and -30e C (or amount of Btu) You need a minimum of 100% at -20e C and 80% at -30e C, and do increase the amount of btu. My electricity bill keep on going down year after year, son much so, that the Electricity provider came last year to change the electric meter as they thought it was defective.
I do not sell those, nor do I work in this field, as I said, I am just fooling around with those.
New refrigerant are coming, and new compressor also, magnetic type, no oil, no friction.
Thanks for sharing all that info Alain. Helpful!
Alain, I’m happy for you in that your experience with heat pumps has been positive. One unanswered question is if you had natural gas available and used it for heat, would your heating cost be more or less than with heat pumps. Most people naturally use the least expensive option. If heat pumps were more economical to use, I wouldn’t think effort to deny natural gas hook ups would be called for.
Natural gas would be way more expensive, I convinced a friend to change his gaz only system to a bi-energy one (heat pump and gaz), gaz would go on only if the heat pump would not be enough in very cold situation and as back-up, (you always need a back-up with heat pumps). Not only the gaz never went on, but the price tag at the end of the year saved him a lot of money, more than 30% saving, compare to gaz only. In Quebec, electricity prices dont fluctuate according to demand, it is the same.
Alain,
Given that you change heat pumps on a regular basis to keep up with the latest technology, here’s an idea for lowering your summer cooling costs…
A cross-flow evaporative unit. There are two air streams. Air is drawn from outside, is evaporatively cooled, it absorbs energy from the indoor air stream, then it is exhausted outdoors. Air from indoors is drawn in, gives up its energy to the outdoor air stream, and is exhausted back indoors.
Thus, no humidity is added to indoor air (and in fact, it can actually cause the indoor air stream to reduce its water vapor load if outdoor humidity is low so the evaporative cooling is especially efficient, and the indoor air stream is reduced in temperature below its dew point).
The cost to run such a beast? A fan and a small pump… about 1/10th the cost of a compressor-driven AC cycle for a commercially-available evaporative unit.
It doesn’t work everywhere, as you need relatively low humidity (< ~50% RH) to get evaporative cooling to work. Coolerado makes such a unit for whole-house cooling.
I provided Coolerado a method by which they could expand the geographic range at which their units could work (essentially, you increase the outdoor airflow speed to force more evaporative cooling, while reducing indoor airflow speed to more effectively cool the indoor air). But that would require some reworking of their units… a variable-speed drive for the fan, a variable-sized camera-shutter type exhaust orifice upstream of the evaporation chamber and the logic to calculate ‘outdoor RH vs. fan speed vs. evaporative cooling capacity vs. indoor temperature’. That would allow their unit to be used even in the Southeast US, where RH is relatively high. I used a similar concept on my own home-built device (located SE TX), and was able to cool the entire house for a mere 80 W of power and about 3 GPH water usage (which I could have gotten even lower if I’d recycled the water runoff, but I just let it water the yard).
Alain, Thank you for your thoughtful contribution to the discussion. I have a question for you, when you increase the BTU capacity as you suggest, does the purchase price of the heat pump go up proportionately (is a unit with 50% more BTU’s 50% more expensive to buy and install?)
Installation is pretty much the same cost for both installation and material. When you change an existing system, most material are already there, sometimes you don’t even have to change the copper pipes, or only one of the two. Labor wise it is the same.
I buy my stuff from the same distributor, being a friend I get very good prices, sometimes at cost. And the price let us say from 18,000btu to 24,000, BTU, is only a few hundred dollar, let us say if I pay $900 for 18,000 (1 ½ ton) I will pay around $1,100 for a 24,000 btu. (Canadian$) and pre-pandemic $, now prices are crazy both for material and labor. You should not expect a 50% increase, but who knows today?
I do the labor myself, having done so for the last 20 years, although, I am not ‘allowed’ to do so. I have all the tools, it took me maximum 2 hours (including 30 minutes of vacuum for pipes) to replace my basement unit last summer which I got for free (my friend ask me to test it). A brand new ‘hyper heat’ system, same brand as the previous one, same amount of BTU. but supposedly higher efficiency. I am not entirely satisfied with it, efficiency start dropping at -15e C, it does not drop as much as the previous one, but still does. As I said, look for a 100% efficiency at -20e C, and ‘pray’. Laboratory and mathematical data is one thing and ‘in reality’ another. Heating, up to -30e C is meaningless unless you have a good efficiency at -30e C. If you get 40-50% efficiency, that is garbage, minimum 80% at -30e C is Ok. Most retailers won’t show you those data. What they show you is data at -8e C which are for cold climate meaningless, because a low efficiency unit, may show the same as the high efficiency at -8e C.
As for summer, only one of the three is on, and it is very good at cooling the whole house and it removes all humidity in the house in a very short time. I have no need to try to make more efficient what is already very good. As the old saying says; if it aint broken, don’t try to fix it.
I am not in a rush to change the basement unit, and will wait another year or two, new refrigerant coming and will wait to hear about performance from ‘valid’ sources. Ideally, I will also wait for magnetic compressor to become widely available. They have been around for a few years now, but haven’t seen any yet in Canada for residential purpose, but I do know they exist.
Be sure, when you’re pulling the vacuum on the system, that you get it down below the 500 micron level… some older vacuum pumps can’t reach that level, but it’s essential in order to get moisture out… leave that moisture in and you get nasty corrosion byproducts that eat your system from the inside.
Once you’ve pulled a vacuum, bottle up the system and watch your pressure gauge for about 12 hours… if it rises above ~500 microns, then stops, you’ve likely got moisture in your system. Just keep pulling it down and waiting 12 hours until it no longer rises.
If it continually rises, then you’ve got a leak.
Also, every time you crack open the system, you should be putting on a new filter-drier.
If the outside air is still, your house is easier to heat.
If heat pumps are eventually fitted to every house and apartment, then during a cold spell they will in effect be cooling the local air very considerably. That is especially the case when wind speed is fairly low, allowing the cooled air to hang around the neighbourhood at ground level (since cool air is heavier than warm). Surely that will mean that all the heat pumps have to work harder to extract what little “heat” remains available. Much the same applies at the summer side of the year if the heat pumps switch to air conditioning mode. Then they pump even more heat into the outside environment and as that warmer air rises then it almost certainly has a noticeable effect on the lower atmosphere circulation.
Tony, that’s an interesting thought. On a very cold day with no wind could a significant cluster of heat pumps compete with each other for the available ambient heat?
This is an excellent article not only for understanding heat pumps but also their limitations. I believe there is one typo. “The outside air temperature is 25°C or colder” should read “The outside air temperature is minus 25°C or colder”.
Thanks. Fixed it. -CCD Ed.
Thanks David and Tom!
This same concept can be applied to the troposphere… while the climate alarmists claim water is a “global warming” gas, it is in fact actually a literal refrigerant (in the strict ‘refrigeration cycle’ sense):
The refrigeration cycle (Earth) [A/C system]:
A liquid evaporates at the heat source (the surface) [in the evaporator], it is transported (convected) [via an A/C compressor], it gives up its energy to the heat sink and undergoes phase change (emits radiation in the upper atmosphere, the majority of which is upwelling owing to the mean free path length / altitude / air density relation) [in the condenser], it is transported (falls as rain or snow) [via that A/C compressor], and the cycle repeats.
The same holds for other polyatomics, to a lesser extent (mainly because at prevalent Earthly temperatures, their latent heat capacity doesn’t come into play, only their relatively higher DOF (as compared to monoatomics) does).
It is the monoatomics and homonuclear diatomics which are the actual ‘greenhouse’ gases… remember that an actual greenhouse works by hindering convection.
Monoatomics (Ar) have no vibrational mode quantum states, and thus cannot emit (nor absorb) IR. Homonuclear diatomics (O2, N2) have no net magnetic dipole and thus cannot emit (nor absorb) IR unless that net-zero magnetic dipole is perturbed via collision.
In an atmosphere consisting of solely monoatomics and homonuclear diatomics, the atoms / molecules could pick up energy via conduction by contacting the surface, just as the polyatomics do; they could convect just as the polyatomics do… but once in the upper atmosphere, they could not as effectively radiatively emit that energy to space, the upper atmosphere would warm, lending less buoyancy to convecting air, thus hindering convection… and that’s how an actual greenhouse works, by hindering convection.
The surface would also have to warm because that ~76.2% of energy which is currently removed from the surface via convection and evaporation would have to be removed nearly solely via radiation (there would be some collisional perturbation of N2 and O2, and thus some emission in the atmosphere)…. and a higher surface radiant exitance implies a higher surface temperature.
So we live, at the planet’s surface, in what can be analogized to the evaporator section of a world-sized AC unit, with H2O playing the part of a literal refrigerant, with other polyatomics (CO2) contributing less to the cooling (because while they have more DOF (Degrees of Freedom) than monoatomics and homonuclear diatomics and can thus transit energy more efficiently than monoatomics and homonuclear diatomics, their latent heat doesn’t come into play at prevalent Earthly temperatures), and with Ar, O2 and N2 playing the same role as noncondensable gases would play in an AC unit… a reduction in the efficiency at which energy is transited from surface to upper atmosphere and emitted to the infinite heat sink of space.
IOW, the climastrologists and climate alarmists have (yet again) flipped reality on its head… they’ve flipped causality. Why? Because the easiest lie to tell is an inversion of reality, a flipped-causality. Most people cannot discern between reality and flipped-causality.
Backradiation? It’s a mathematical artifact due to misuse of the Stefan-Boltzmann equation.
Force: [M1 L1 T-2] /
Area: [M0 L2 T0] =
Pressure: [M1 L-1 T-2] /
Length: [M0 L1 T0] =
Pressure Gradient: [M1 L-2 T-2]
Energy: [M1 L2 T−2] /
Volume: [M0 L3 T0] =
Energy Density: [M1 L-1 T-2] /
Length: [M0 L1 T0] =
Energy Density Gradient: [M1 L-2 T-2]
Pressure and energy density are two forms of the same thing (note the identical dimensionality above), just as pressure gradient and energy density gradient are two forms of the same thing.
Thus, just as, for instance, water only spontaneously flows down a pressure gradient (ie: downhill), energy only spontaneously flows down an energy density gradient. This is reflected in 2LoT in the Clausius Statement sense.
Energy density is a pressure, energy density gradient is a pressure gradient… for energy.
https://i.imgur.com/QErszYW.gif
Idealized Blackbody Object (assumes emission to 0 K and ε = 1 by definition):
q_bb = ε σ (T_h^4 – T_c^4) A_h
= 1 σ (T_h^4 – 0 K) 1 m^2
= σ T^4
Graybody Object (assumes emission to > 0 K and ε < 1):
q_gb = ε σ (T_h^4 – T_c^4) A_h
The ‘A_h’ term is merely a multiplier, used if one is calculating for an area larger than unity [for instance: >1 m^2], which converts the result from radiant exitance (W m-2, radiant flux per unit area) to radiant flux (W).
Temperature is equal to the fourth root of radiation energy density divided by Stefan’s Constant (ie: the radiation constant).
e = T^4 a
a = 4σ/c
e = T^4 4σ/c
T^4 = e/(4σ/c)
T = 4^√(e/(4σ/c))
T = 4^√(e/a)
q = ε σ (T_h^4 – T_c^4)
∴ q = ε σ ((e_h / (4σ / c)) – (e_c / (4σ / c))) Ah
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = W m-2 K-4 * (Δ(J m-3 / (W m-2 K-4 / m sec-1)))
∴ q = (ε c (e_h – e_c)) / 4
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = (m sec-1 (ΔJ m-3)) / 4
One can see from the immediately-above equation that the Stefan-Boltzmann (S-B) equation is all about subtracting the radiation energy density of the cooler object from the radiation energy density of the warmer object.
∴ q = σ / a * Δe
Canceling units, we get W m-2.
W m-2 = (W m-2 K-4 / J m-3 K-4) * ΔJ m-3
For graybody objects, it is the radiation energy density differential between warmer object and cooler object which determines warmer object radiant exitance.
Do keep in mind that a warmer object will have higher energy density at all wavelengths than a cooler object:
https://i.stack.imgur.com/qPJ94.png
Warmer objects don’t absorb radiation from cooler objects (a violation of 2LoT in the Clausius Statement sense and Stefan’s Law); the lower radiation energy density gradient between warmer and cooler objects (as compared to between warmer object and 0 K) lowers radiant exitance of the warmer object (as compared to its radiant exitance if it were emitting to 0 K). The radiation energy density differential between objects manifests a radiation energy density gradient, each surface’s radiation energy density manifesting a proportional radiation pressure.
CAGW is a scam built upon mathematical fraudery… as most of the climate alarmist agenda is.
In fact, the Kiehl-Trenberth ‘Earth Energy Balance’ graphic (and all subsequent similar graphics), which are representations of the mathematics used in Energy Balance Climate Models (EBCMs) does exactly this sort of mathematical fraudery… it treats a real-world graybody surface as though it’s an idealized blackbody object (with emission to 0 K and emissivity = 1)… it isolates each object into its own system so the objects cannot interact via the ambient EM field.
That’s the only way the Kiehl-Trenberth diagram can get to 390 W m-2 surface radiant exitance.
Doing so inflates radiant exitance of each object, necessitating that the climastrologists subtract a wholly-fictive ‘cooler to warmer’ energy flow from the real (but far too high because it was calculated for emission to 0 K) energy flow.
That ‘cooler to warmer’ energy flow is the mathematical artifact due to misuse of the S-B equation. It’s not real.
“But they’ve measured backradiation!”, some may protest… yeah, no.
https://claesjohnson.blogspot.com/2011/08/how-to-fool-yourself-with-pyrgeometer.html
As Professor Claes Johnson shows in that article on his website, pyrgeometers (the instrument typically used to ‘measure’ backradiation) utilize the same sort of misuse of the S-B equation as the climastrologists use. The bastardized form of the S-B equation used by pyrgeometers [ usually some form of q = (σ Th4 – σ Tc4) or equivalently Ld = Uemf/S + σTb, as outlined in the documentation for the instrument, with Uemf/S being negative in sign ] apriori assumes a subtraction of ‘cooler to warmer’ energy flow from ‘warmer to cooler’ energy flow, which as has been shown, is fallacious.
Do remember that photons, each a quantum of energy, are considered the force-carrying gauge bosons of the EM interaction.
Going back to dimensional analysis:
We start with Energy: [M1 L2 T−2] –
Force: [M1 L1 T-2] *
Length: [M0 L1 T0] =
[M0 L0 T0]
We are left with nothing on the ‘transmitting’ end… [M0 L0 T0]. In other words, that Energy is used to apply a Force along a Length. It’s obvious then, that if an equal and opposing Force were applied along that Length, no energy can flow… this is just as true radiatively as it is mechanically.
That Force applied along a Length gives us (on the ‘receiving’ end):
Force: [M1 L1 T-2] *
Length: [M0 L1 T0] =
Work: [M1 L2 T-2]
You’ll note that Energy and Work have the same units:
Work: [M1 L2 T-2] = Energy: [M1 L2 T−2]
For those who want to put it in terms of Momentum:
Momentum: [M1 L1 T−1] *
Velocity: [M0 L1 T-1] =
Work: [M1 L2 T−2]
That means Energy Expended = Force * Length = Momentum * Velocity = Work
There’s a reason for that. Free Energy is defined as that energy capable of performing work. This is reflected in the equation for Free Energy (represented here as a single object and its environment):
F = U – TS + PV
Where: F = Free Energy; U = internal energy; T = absolute temp; S = final entropy; TS = energy the object can receive from the environment; PV = work done to give the system final volume V at pressure P
If U > TS + PV, F > 0… energy must flow from object to environment.
If U = TS + PV, F = 0… no energy can flow to or from the object.
If U < TS + PV, F < 0… energy must flow from environment to object.
Of course, if we were talking about a system with only two objects with the same physical parameters and nothing else in the system, we could represent the Free Energy as: F = U1 – U2
Which is better represented as internal energy over volume to get energy density (since internal energy is an extensive property), converting the calculation to that of an intensive property and thus allowing us to compare dissimilar-sized objects: F = U1/V1 – U2/V2 = e1 – e2
And that’s exactly what the S-B equation does. Remember that temperature is a measure of radiation energy density, equal to the fourth root of radiation energy density divided by the radiation constant (Stefan’s Constant). Remember that I wrote above:
∴ q = (ε c (eh – ec)) / 4
Canceling units, we get J sec-1 m-2, which is W m-2 (1 J sec-1 = 1 W).
W m-2 = (m sec-1 (ΔJ m-3)) / 4
One can see that the S-B equation is all about subtracting the radiation energy density of the cooler object from the radiation energy density of the warmer object (to arrive at the radiation energy density gradient) because Free Energy is all about subtracting the energy density of one object from the energy density of the other object (no matter the form of that energy).
There are several other methods of disproving the CAGW hypothesis, such as entropy, but we’ll leave that for another time.
LOL@Klimate Katastrophe Kooks wrote:
“We are left with nothing on the ‘transmitting’ end… [M0 L0 T0]. In other words, that Energy is used to apply a Force along a Length. It’s obvious then, that if an equal and opposing Force were applied along that Length, no energy can flow… this is just as true radiatively as it is mechanically.”
{ You will note that the text below definitively destroys the CAGW hypothesis… I’ve debated many climastrologists and warmist physicists… none have prevailed against the scientific reality below, and some have even changed their stance in light of that scientific reality. }
Now, why does it happen in this manner?
Well, what I’ve described above would be referred to as thermodynamic equilibrium… a stream of photons at a certain wavelength in one direction, a stream of photons of the same wavelength in the exact opposite direction (ie: equal and opposing forces)… and what is that? It’s a standing wave by definition.
One problem the climastrologists struggle with is that their take on radiative energy exchange necessitates that at thermodynamic equilibrium, objects are furiously emitting and absorbing radiation (this is brought about because they claim that objects emit only according to their temperature (rather than according to the radiation energy density gradient), thus for objects at the same temperature in an environment at the same temperature, all would be furiously emitting and absorbing radiation… in other words, they claim that graybody objects emit > 0 K), and they’ve forgotten about entropy… if the objects (and the environment) are furiously emitting and absorbing radiation at thermodynamic equilibrium as their incorrect take on reality must claim, why does entropy not change?
The second law states that there exists a state variable called entropy S. The change in entropy (ΔS) is equal to the energy transferred (ΔQ) divided by the temperature (T).
ΔS = ΔQ / T
Only for reversible processes does entropy remain constant. Reversible processes are idealizations. All real-world processes are irreversible.
The climastrologists claim that energy can flow from cooler to warmer because they cling to the long-debunked Prevost Principle, which states that an object’s radiant exitance is dependent only upon that object’s internal state, and thus they treat real-world graybody objects as though they’re idealized blackbody objects via: q = σ T^4 (sometimes they slap ε onto that… which is still a misuse of the S-B equation, for graybody objects) .
… thus the climate alarmists claim that all objects emit radiation if they are above 0 K. In reality, idealized blackbody objects emit radiation if they are above 0 K, whereas graybody objects emit radiation if their temperature is greater than 0 K above the ambient.
But their claim means that in an environment at thermodynamic equilibrium, all objects (and the ambient) would be furiously emitting and absorbing radiation, but since entropy doesn’t change at thermodynamic equilibrium, the climastrologists must claim that radiative energy transfer is a reversible process. Except radiative energy transfer is an irreversible process, which destroys their claim.
In reality, at thermodynamic equilibrium, no energy flows, the system reaches a quiescent state (the definition of thermodynamic equilibrium), which is why entropy doesn’t change. A standing wave is set up by the photons remaining in the intervening space between two objects at thermodynamic equilibrium, with the standing wave nodes at the surface of the objects by dint of the boundary constraints (and being wave nodes (nodes being the zero crossing points, anti-nodes being the positive and negative peaks), no energy can be transferred into or out of the objects). Should one object change temperature, the standing wave becomes a traveling wave, with the group velocity proportional to the radiation energy density differential, and in the direction toward the cooler object. This is standard cavity theory, applied to objects.
All idealized blackbody objects above absolute zero emit radiation, assume emission to 0 K and don’t actually exist, they’re idealizations.
Real-world graybody objects with a temperature greater than zero degrees above their ambient emit radiation. Graybody objects emit (and absorb) according to the radiation energy density gradient.
Thus it is obvious that at thermodynamic equilibrium, there is no emission nor absorption. The standing wave is set up by photons which remain in the intervening space at the point where the objects come into thermodynamic equilibrium, and are perfectly reflected by the objects thereafter until thermodynamic equilibrium is broken (proof below).
It’s right there in the S-B equation, which the climate alarmists fundamentally misunderstand:
https://i.imgur.com/QErszYW.gif
All real-world processes are irreversible processes, including radiative energy transfer, because radiative energy transfer is an entropic temporal process.
“If your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.”
– Arthur Eddington: The Nature of the Physical World. (1929)
Their mathematical fraudery is what led to their ‘energy can flow willy-nilly without regard to radiation energy density gradient‘ narrative (in their keeping with the long-debunked Prevost Principle), which led to their ‘backradiation‘ narrative, which led to their ‘CAGW‘ narrative, all of it definitively, mathematically, scientifically proven to be fallacious.
A further proof:
Do remember that temperature (T) is a measure of radiation energy density (e), equal to the fourth root of radiation energy density divided by Stefan’s Constant.
As Δe → 0, ΔT → 0, q → 0. As q → 0, the ratio of graybody object total emissive power to idealized blackbody object total emissive power → 0. In other words, emissivity → 0. At thermodynamic equilibrium for a graybody object, there is no radiation energy density gradient and thus no impetus for photon generation.
As Δe → 0, ΔT → 0, photon chemical potential → 0, photon Free Energy → 0. At zero chemical potential, zero Free Energy, the photon can do no work, so there is no impetus for the photon to be absorbed. The ratio of the absorbed to the incident radiant power → 0. In other words, absorptivity → 0.
α = absorptivity = absorbed / incident radiant power
ρ = reflectivity = reflected / incident radiant power
τ = transmissivity = transmitted / incident radiant power
α + ρ + τ = 100%
For opaque surfaces τ = 0% ∴ α + ρ = 100%
If α = 0%, 0% + ρ = 100% ∴ ρ = 100% … all incident photons are reflected at thermodynamic equilibrium for graybody objects.
This coincides with standard cavity theory… applying cavity theory outside a cavity, for two graybody objects at thermodynamic equilibrium, no absorption nor emission takes place. The photons remaining in the intervening space set up a standing wave, with the wavemode nodes at the object surfaces by dint of the boundary constraints. Nodes being a zero-crossing point (and anti-nodes being the positive and negative peaks), no energy can be transferred into or out of the objects. Photon chemical potential is zero, they can do no work, photon Free Energy is zero, they can do no work (and thus cannot be absorbed). Should one object change temperature, the standing wave becomes a traveling wave with the group velocity proportional to the radiation energy density gradient and in the direction of the cooler object.
I’ve had some physicists attempt to get tricky by claiming that a photon from a cooler object, emitted at a higher wavelength, could be absorbed by a warmer object which has an unexcited resonant quantum state. Yeah, no.
As stated in my prior post:
Do keep in mind that a warmer object will have higher energy density at all wavelengths than a cooler object:
https://i.stack.imgur.com/qPJ94.png
My sister has had a heat pump for more than 30 years. Why? There’s no natural gas available to her residence.
Every time you convert energy, you lose some (inefficient). Why use Nat gas to generate electricity (40 to 60% efficiency, not counting line losses) when a home Nat gas furnace is 90% efficient? Of course, subsidies and taxes are deliberate distortions in any calculation. If you choose to use electricity for all your household energy needs, you’ve walked straight into the socialists trap. Smart meters and rolling black outs will be their leash on you.
We live where the only utility available is electricity. I added propane to the house for both heating and hot water. That has worked very well for 24 years. Even though we live where electricity is less expensive because most power is hydroelectric, the cost of any kind of electric heat is much higher than propane.
Adding propane to the house rather than replacing electric with propane turned out to be very wise. Sometimes propane can not be delivered for extended periods of time due icy conditions on our steep roads.
I did not mention that my sister’s system is buried in an acre of clay. Geothermal, kind of. I’m considering a similar set up, deeper over a larger area. Not everyone has the angles I have. Outdoor firewood furnace plus acreage. I will avoid carbon taxes anyway I can.
Yes, if you’ve got a ground-source heat pump, it can remain operational even when outdoor temperature dips below the refrigerant temperature, but you’ve got to bury the heat exchanger lines far below the frost line (and the further north you go, the deeper you have to go) and the larger your heat exchange field is, the better (except it can get expensive unless you rent a trench digger and do that work yourself).
Where I grew up, we buried our lines (water lines from the well and the heat exchanger lines) 6 feet deep, about 1 foot below the frost line. You might have to go as much as 10 feet deep in far northern climes.
https://www.familyhandyman.com/wp-content/uploads/2021/06/FrostLineMap.jpg
But the ultimate method of saving energy is to super-insulate the home… they’ve got new vacuum insulated panels (VIP) that provide R28 insulation value… a couple of those back-to-back, along with weatherproofing so there’s less air infiltration / exfiltration, and it really drops the amount of energy required to heat / cool the house.
Older houses can have as many as 4 air exchanges per hour (laypeople would say they are ‘drafty’)… if you can get it down to 0.35 air exchanges per hour (the ASHRAE recommendation), it’ll drop your energy bill.
One tactic is to get the natural air exchange rate as close to zero as possible, then use a cross-flow heat exchanger to exchange fresh outdoor air for stale indoor air, while transferring the energy of the air from incoming to outgoing or vice versa. On a cold day, that would use the warmer temperature of the exhausted air to warm the incoming air. On a warm day, it would use the lower temperature of the outgoing air to cool the incoming air.