Tom Napier makes a scientific evaluation of Dennis's machine

Tom Napier makes a scientific evaluation of Dennis's machine

created 9/23/96, last updated 5/25/01 -this page accessible as

The Myth of Free Energy, a Reply to "Santiago". Copyright 1996 by T. M. Napier, all rights reserved.

My original article on free energy (A Glimpse of Cloud-cuckoo-land, Phactum, October 1996) was constrained by two considerations. It had to fit into a limited space in a magazine and it had to be reasonably comprehensible to a non-scientific audience. I thus took some care to make it clear and to get the facts correct. It would pay to read it again, very carefully.

It was based entirely on what I saw and heard at Dennis Lee's demonstration. It was not until after it had appeared in print that I found that Mr Lee had spent some time in jail and that he has been demonstrating "better technology" since 1987 without ever producing a working free energy machine. The latter fact casts doubt on his claims to be shipping working units by this Christmas.

Efficiency is a tricky subject and one has to be very careful not to compare apples and oranges. The textbook definition of a 100% efficient process is one which can be reversed. For example, if one had a 100% efficient machine for converting mechanical power into heat energy one could run it backwards to convert the heat energy back into mechanical energy. Given two such machines, one converting mechanical energy to heat energy and the other converting this heat energy back to mechanical form, one would get back out exactly as much energy as one put in. Of course any losses due to friction in the mechanical part or to unintended cooling in the heat part of either machine would result in one or both having less than 100% efficiency.

As it happens, one can convert backwards and forwards between electrical power and mechanical power with quite low losses, a good electric motor can be 95% efficient, thus one could put electric power into one machine and get electric power back out of the other. However the power out can only approach 100% of the power in and it certainly cannot exceed 100%.

Here is where the confusion arises. Energy can be measured in several different ways, depending on what one is measuring. For example, mechanical energy can be measured in foot.pounds, the energy required to exert a force of one pound through a distance of one foot. (Exerting a force on something which does not move requires no energy. This is why a demonstration of an enormous torque is not evidence of great energy.) For convenience I will use the equivalent metric units where energy is measured in Newton.meters. (One Newton.meter = 0.7376 foot.pounds) My reason for the switch is that one Newton.meter is equal to one Joule and the Joule is the unit in which electrical power is measured. One Joule is a power of one watt for one second.

The electric company measures power in kilowatt.hours, it should be obvious that one kilowatt.hour is 3,600,000 Joules. This is 3,600,000 Newton.meters or 2,655,360 foot.pounds. This indicates that one kilowatt.hour of electricity could lift a thousand pound weight through 2655 feet. Since electric motors are very efficient converters between electrical energy and mechanical energy this is close to what would happen in real life. By the way, one kilowatt is about 1.3405 of a horsepower so a 1.34 horsepower motor could raise the same weight the same distance in one hour of running. (Let's check my arithmetic: One horsepower is 550 foot.pounds per second so one horsepower for one hour is 1,980,000 foot.pounds and 1.34 horsepower for one hour is 2,654,155 foot.pounds which is almost exactly what I got by the first computation. Good.)

Heat energy is measured in calories if you are a scientist and in BTU if you are a heating engineer. One calorie is the heat energy needed to raise the temperature of one gram of water through one degree Celsius. The BTU is is the heat energy needed to raise the temperature of one pound of water through one degree Fahrenheit. One BTU equals 252 calories. (The "Calorie" used by the diet-conscious is actually a kilo-calorie, the energy needed to raise one kilogram of water by one degree Celsius.)

This is where apples and oranges come in. What electrical or mechanical energy is equivalent to a given amount of heat energy?

One way of measuring this is to dissipate energy in water and to measure how much its temperature rises. You could put a resistance heater in a cup of water, measure the electrical power in and measure the resulting temperature rise in the water. Similarly, you could put a little paddle in the water, measure how much power it takes to turn it and again measure the temperature rise. One does experiments like these in the first year of a college physics course. They measure the "mechanical equivalent of heat" which happens to be 4.186 Joules per calorie. From this number one can work out useful things, for example, how long it takes a 1000 watt kettle to boil a pint of water.

Unfortunately, while processes like these can convert electrical or mechanical energy to heat energy, there is no equivalent process for converting it back again. Even though all of the input energy went into the the water, something has been lost, the ability to get back one's original energy. In fact, if one wants to convert mechanical energy into heat energy there is a better way of doing it. This is where the heat pump comes in.

The nice thing about heat engines is that they work both ways. You can use the same machine to convert heat into mechanical power or to convert mechanical power into heat. A heat engine running forwards takes heat energy in at one temperature, rejects heat energy at a lower temperature and converts all of the energy difference into mechanical energy. You can't ask for a better performance than that. To get heat to flow though the machine you need both a source of heat energy at one temperature and a sink at a lower temperature to which you can transfer heat energy. If the quantity of heat flowing in is Qh and the quantity of heat flowing out is Ql the output energy (Qo) is Qh-Ql. We can define the efficiency of the machine as (Energy out)/(Energy in) or (Qh-Ql)/Qh. Note that since Ql is greater than zero the efficiency of the conversion is always less than 100%. This isn't even physics, it is true by definition.

One way of making a perfect heat engine is to circulate a gas through two pistons and cylinders so that the pressure and temperature of the gas follow what is called the Carnot cycle. No real Carnot cycle engine has been build though some types of engine come close. Their efficiencies are all lower than the ideal even if you ignore things like friction and heat loss.

To say that a conversion is 50% efficient is no more mysterious than to say that if I have a pint of beer and I lower its level halfway, I have only drunk 50% of my beer. If I drank the beer to the bottom I would have drunk 100% of it. You can no more have a machine which is more than 100% efficient than you can drink more than a pint from a pint mug.

Write the efficiency as (1-Ql/Qh). Since the heat engine works by heating and cooling a fixed amount of material we can represent the ratio of the two amounts of heat as the ratio of the absolute (Kelvin) temperatures of the source and the sink. We get Efficiency = (1-Tl/Th). (There's nothing funny about this step, zero degrees Kelvin (-459.7 F) is defined to be the starting point which makes this relationship true. That 0K is also the point where gas volumes go to zero and molecular motion ceases is interesting but irrelevant in this context.)

What this says is that if you generate heat by burning fuel or by electrical heating, the amount of this energy which can be converted back into mechanical energy is less than you put in. The limit is a function of how hot you can make the source and how cold you can make the sink. Usually the sink temperature is fixed by one's environment, the local air or water temperature, so the best thing one can do is to use as high a source temperature as possible. There one runs into limitations such as the temperature a flame will reach, the pressure one's boiler can stand or the melting point of ones metals. A steam engine can run at a temperature of perhaps 500F (960K). Given a cooling water temperature of 70F (530K) its best possible efficiency is 1-530/960 = 44.8%.

Just for the record, power stations do use a closed loop system, they use contaminant-free water in the boilers and condense the steam back to water in cooling towers. They use turbines because turbines are more efficient than reciprocating steam engines, mainly because a turbine can handle a higher input temperature and pressure than a piston engine.

If you run a heat engine backwards, by putting in mechanical energy, it will get cold at one end and hot at the other. If you supply heat energy at the cold end, you can take more heat energy out at the hot end than you put in at the cold end. The equation which describes this, Qh = Ql+Qi, is exactly the same as the equation which describes the heat engine running forwards except that I've called the mechanical term Qi (for input) rather than Qo (for output). This is why heat engines are described as being "reversible" engines. They perform equally well in both directions.

Qh = Ql+Qi is the fundamental equation of the refrigerator or of the heat pump. Mechanical energy "pumps" heat from a place at one temperature to another place at a higher temperature. In a refrigerator the high temperature is room temperature and the object is to make something cold. Since we are interested in how much cooling we get, we regard Ql as the useful output. The input is Qi so we can define a Quality Factor which is Ql/Qi. Since Qi = Qh-Ql the quality factor of a refrigerator is Ql/(Qh-Ql). Since this equals Tl/(Th-Tl) we can see that the quality factor of a refrigerator running between an 80F outside and a 0F inside is 460/80 or 5.75. Of course, this is the ideal performance, assuming a 100% efficient compressor, no friction and heat exchangers which work with no temperature differential. These are all areas where improvements in technology can be made. This will improve the quality factor but cannot make it exceed its theoretical value.

The other application for a backwards heat engine is the heat pump (At last.) This is just a refrigerator run between the outside temperature and the inside temperature of a house. Since this time we are interested in how much heat it puts out (Qh) we can define its Quality Factor to be Qh/Qi or Qh/(Qh-Ql). Using the same numbers as last time, 80F inside the house and 0F outside, the quality factor is 540/80 which is 6.75. (The QF of a heat pump is one higher than the QF of a refrigerator. This is because we are interested in the output of heat in one case and in the output of cold in the other. The input energy contributes to the heat but not to the cold.) The quality factor depends on how cold the outside air is. If the outside air was 32F rather than 0F the QF would be 540/48 which is 11.25. If one uses a solar collector for the outside unit it can be hotter than the air temperature, this improves the QF. Again, these are theoretical limits, a real heat pump would not be quite as good.

This Quality Factor is where the "600% efficiency" comes from. What it means is that the heat energy output is, say, six times the mechanical (or electrical) energy input. This doesn't really mean that you have gained energy, it just means that when we defined the "mechanical equivalent of heat" the method used to convert mechanical energy to heat energy was not the most efficient possible way of doing so. It is a convenient method for making measurements since the result does not depend on the absolute temperature, but it is not the best way to get heat. This is why I said in my article that a heat pump is six times more efficient than a convector heater. This does not imply that a heat pump has a 600% efficiency, only that a convector heater is much less efficient than a heat pump in terms of heat out for electrical power in.

Remember, there is no process to convert the mechanical equivalent of heat directly back to mechanical energy. The only way we can convert the output of a heat pump back into electrical energy is by connecting it to another heat engine.

Let's do the calculation. I'll use actual numbers here rather than doing the job algebraically but the end result doesn't depend on the numbers used. Let's take your numbers, 0F and 250F. These are 460K and 710K so the heat pump's quality factor is 710/250 which is 2.84. Note that, because of the higher temperature difference, this is much lower than in a typical heat pump application.

Now that we have a source of 250F heat we will apply it to any heat engine you can imagine using whichever working fluid you please. Some of these will be pretty lousy machines so I'm going to apply this heat source to a perfect machine instead. It is going to take in heat energy at 250F. The output power depends on how little heat power we waste so we will use the lowest available temperature sink, the same outside air at 0F with which we started. A perfect heat engine running between 250F and 0F has an efficiency of 250/710 which is 35.2%. Now our gain from the heat pump was 2.84 so let's multiply this by .352 and see how much energy we get back out.

Oops, rounding error, it's 0.9968. Since this number is really the gain, 710/250, multiplied by the efficiency, 250/710, you can see that the energy out is always exactly equal to the energy in. In other words, the heat pump's gain is Th/(Th-Tl) and the generator's efficiency is (Th-Tl)/Th. The product of these is always unity regardless of the actual values of Th and Tl. Sorry about that, but there's never anything left over to sell to the utility company.

There is s tiny loophole, if the external collector is warmed by the sun and the engine's cooler is not, there will be a gain in energy corresponding to the solar power input. However, this could be extracted more efficiently by running a heat engine directly between the "hot" collector and the cold air. Its efficiency will be dreadfully low since the temperature difference is small but it will generate some energy. It's not "free energy" for all that.

One can complicate matters by using a material which changes from a liquid to a gas and back again. A condensing gas gives out the energy of its latent heat and it requires an energy input to evaporate the resulting liquid. This makes it easier to transfer heat from place to place but it should be obvious that the two energies, input and output, are equal. There are some practical advantages, for example, it is easier to heat and cool a liquid, it can pass through smaller pipes and it is much easier to pump.

One thing people forget about steam engines is that they have two piston systems, not one. The boiler is under pressure and the steam coming out has a much higher volume than the water which is pumped in by the return pump. Thus the energy supplied by a given mass of water in the form of hot, high pressure steam is much more than the energy required to pump that mass of water back into the boiler after it is condensed. However, no amount of hand-waving about low temperature phase changes and fluids which "burst into steam" can cover up the fact that any energy which can be extracted from a boiling liquid must have been put into it from somewhere. If any of that energy is used up by driving a generator it has to be replaced. Any energy which is left in the working fluid, while it makes it easier to heat it again, also reduces the efficiency since it is the equivalent of raising the sink temperature. Once more, Th/(Th-Tl) times (Th-Tl)/Th always equals 100%.

My point about the zeromotor was two-fold. Firstly I was pointing out that Mr Lee is not introducing "new technology", he is covering the same ground as many failed perpetual motion inventors before him. My other point was that the US Navy is still, last I heard, driving its ships with oil or nuclear power. If there was a way of generating power from sea water don't you think they would be using it? Our 100 years of advances in refrigeration don't seem to have done them much good.

Remember, the alchemists failed to convert lead to gold not because no experimenter happened to hit on the right process but because it is not possible using chemical methods. If Dennis Lee really could build a free energy machine he wouldn't need to put on his shows. All he would need to do is to call a press conference and to demonstrate a working model. If he demonstrated an isolated device which could, for example, power a 100 watt bulb continuously, the press might be skeptical at first. However, if the bulb was still running a week or a month or a year later a lot of people, including myself, would be very impressed. Unfortunately, the Second Law of Thermodynamics (recently described as the most depressing scientific discovery of all time) says that this cannot happen.

extra commentary by Eric

Since 1997, the pro Dennis people seem to have given up arguing based on science. Unfortunately, most have limited background and Dennis has left them to fend for themselves. Pro Dennis people seem more comfortable arguing conspiracy theory or Dennis's integrity. To me the only significant question is Does the Technology work? Dennis seems to dance right by this serious open question in his tapes, literature and show. He mentions people with credentials who worked with him at one time, but none seem willing to talk with me. -seems strange becuase all other vangaurd science I know is debated back and forth in an open forum.

back to Eric's main Dennis Lee page

Tom Napiers review of the Philly show

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