Energy fundamentals

Some facts about energy and the Earth

During the renaissance time from the 14th to the 17th century in Europe many people rediscovered the ancient knowledge that came from the Greek, Islamic and Roman history through the works of scholars that went in the libraries of ancient monasteries and translated the old texts and made them available to a wider audience.

This process ended somewhat in the foundation of modern science where the people started to gather information about the world by experiment, meaning a measuring apparatus and a reproducible scenario to obtain certain reproducible data. One of the items under test was fire aka heat. The easiest experiment was to heat water of course. It was found that to heat water from ice to boiling point always took the same amount of heat, independent from the source of the heat. It was agreed then between the scientists that this temperature rise should be divided in 100 degrees Celsius and the heat required to heat 1 gram of water by 1 degree Celsius shall be called one calorie

Later electricity was found and other laws of physics and the measuring unit Joule was introduced for all forms of energy. This unit also applies to heat as one form of energy and the unit calorie was replaced by Joule. That was at the end of the 19th century.

Of course at that time the British empire was the largest empire known to the Europeans and the British did not accept to use a measurement that was not related to the feet et al of the king. That is why they and the Americans until today use a different heat measurement unit called the British thermal unit or BTU

These three units of measurement still exist until today, the Joule however is the only “universal unit” and engineers and scientists working in an international environment only use the SI-unit Joule (J).

With the discovery that water steam still can be heated more and thus increases it’s pressure, people like James Watt invented the steam engine and for the amount of heat a given engine can transform into work in a certain period, the unit Joule per second (J/s) aka Watt was used.

When a (small) steam engine could perform the work of transforming heat of 1000 J per second for a period of one hour the unit kilo Watt-hour (1 kWh) was used. This means burning coal that contains a certain amount of “chemical energy” and shoveling in this or that amount of coal each second.

You might guess that the work of one kWh already is a lot, when people had to constantly shovel in coal
. The first steam engines James Watt built had a thermal efficiency of about 10%. That means, the theoretical amount of heat “inside the coal” had only be transformed to “work” at a tenth of the input. These engines were used to pump out water from deep coal mines as the “easiest” coal started to be depleted and the people had to dig below ground water levels where more coal was to be found. Although a lot of coal had to be shoveled into Watt’s engines, it still was more profitable to dig deeper and in the end have a net gain of coal from that operation.

Later people thought about attaching a generator to a steam engine to produce electric energy that was mainly used for lighting. The generator in general uses the mechanical force of the steam engine to pump the electrons against a resistor (the electric grid). These generators have a so called electrical efficiency of about 98% today and the mechanical energy from the steam is nearly entirely converted into electrical energy that has the unit Volt * Ampere * second (1 VAs = 1 J), so a machine producing electricity with the Voltage of 1 V and the current of 1 A for a period of 1 second “works” 1 Joule (J)

When we consume electricity in our homes, we measure the “work” that we buy from the electricity company in kWh (kilo Watt hours).

So here we start to get into troubles with Joules and kWh.


A modern Computer roughly consumes 100 W or 0,1 kW, a historic light bulb with 100 W transformed electrical energy back into heat (glows hot) at a rate of 100J/s (Joules per second = Watt W).

An electrical appliance working at the power of 0,1 kW for one hour actually consumes 0,1 kWh.

A human body when he sits quiet in a chair roughly “works” at 100 Watts (100W = 0,1 kW = 100J/s). That mostly means, he looses heat at that rate and his metabolism constantly has to burn “food” to keep warm. The temperature of a human normally is 37 degrees Celsius.

When you sit in a chair reading for one hour, your body will have burned roughly 0,1 kWh

When you light a match, you first need to strike it. That means you have to give the wood some starting energy to start the reaction of burning the wood. The human body is built in a way that it maintains 37 degrees Celsius to help “kick start” the chemical reactions in the body easier.

If we had a higher temperature, we might be able to perform more work in a shorter period of time (we could produce more Watts = J/s) but that would have come with the cost that we needed to eat more to keep the temperature up or that the loss during cold days is very high (hotter surface radiates more energy per second). So humans during their evolution have found an optimum operating temperature that helps to run chemical reactions quick but not too warm what is too costly in terms of food.

The energy your body “burns down in a cold reaction” is more or less some form of sugar. There is no fire in your cells because the process is mainly handled by ATP that works as a catalyst that the reactive temperature does not get too hot. So when you start to do some heavy work like running after a Gazelle in the steppe, your body burns down the sugar reserves in your cells until they mainly are depleted and you can no longer run. There comes a tiny little problem with it:

Your body must get rid of waste heat.

Humans are amongst the few animals in the world that can sweat to get rid of waste heat. That permits a higher constant rate of metabolism for a longer period of time and therefore, humans can hunt down a Gazelle by running after her for a long distance and not being exhausted as the Gazelle will be. All other animals rely on silent approaching as close as possible and then use a short sprint to overwhelm the target and kill it. Lions do not run after their prey. When they miss it they go for a second try. Their body simply does not permit to get rid of that much of waste heat.


1. The harder we work, the more we must get rid of waste heat (sweat)

2. To get rid of heat, humans can evaporate water

Ad 1. It has actually been found that any process in the known universe that converts heat into work must produce some waste heat and must find a place to put that waste heat. This is the first law of thermodynamics

We will be back at that later.

Ad 2. When water evaporates, it takes with it a certain amount of energy what is called latent heat. This heat is practically the amount of energy needed to transform ice into water or water into steam (gas) whereby both differ in size, the amount is significant. It is even more significant when the water contains some salt, and nature has given us that trick for our survival.

How much work can we humans really perform ?

If you go to a fitness studio you might find a fixed bicycle that you can adjust in difficulty and tread for one or two hours. If the meter works with Watts, you can go and have a try to tread the bike at 250 Watts for one hour. That usually is an amount only very well trained persons can achieve. When you are not trained, you might not be able to tread the bike at 200 Watts for more than 15 minutes until your metabolism is exhausted.

So let’s assume, you are well trained and you tread the bike at 250 Watts for one hour. Then you will have performed the work of 0,25 kWh and you can give it a try, this will really exhaust you!

Humans do not sit on bikes the whole day, they work for about 8 hours. We find that “office” humans can not work at more than 80 Watts for eight hours, that makes 0,64 kWh.

conversion factor kJ to kWh: 1 kWh = 1000 kJ / 3,6 kJ/kWh

Humans are not able to perform the work of 1 kWh in a single day additionally to their base consumption of roughly 1,75 kWh per day.

Mean base metabolism is 6300 kJ/d = 1,75 kWh/d (d = day)

Work ( J or kWh) is power (Watt W or Joule per second J/s) multiplied by time (seconds or hours)

1 J = 1 Watt W * 1 Time s = 1 J/s * s

A human is more or less a heat engine, that burns down sugar obtained from food with the usage of water and O2, that exhausts CO2.

When we climb up a staircase we adjust the speed that we will not be exhausted. When you run up the staircase you will need a higher power level but for a shorter period of time. The higher power results in increased waste heat (you sweat) but in a shorter time. The actual work you performed is always the same, you moved some kilos of your body up some floors. You can adjust the power you want to use for it, resulting in different times until you are at your apartment door. The energy you used equals the work you did and is always the same. You only applied different “power levels”.

Here you can see what power level is required to toast bread:

So here we find out an important aspect of the transition to renewables:

When we want to work a lot in a short period of time, we will need a higher power level provided (Watts) but the energy being used will be the same if we worked at a lower power level for a longer period of time.

Now we want to address the first & second law of thermodynamics a bit deeper:

The first law actually says that a heat engine that does mechanical work in every possible process produces some sort of waste heat and that is the reason why a perpetual motion machine is impossible.

The second law of thermodynamics more or less says that a hot item will eventually become cold and a cold item can not become hot without energy being applied.

These laws come to another conclusion that is very important for every machinery that converts heat into work:

The maximum theoretical achievable thermal efficiency (Greek letter eta) of the process is

eta = 1 – (T1 / T2)

T2: maximum temperature in the engine in Kelvin

T1: Minimum temperature where the waste heat goes in Kelvin

Kelvin : Kelvin K equals degree Celsius + 273,15. 20 degrees Celsius is 293,15 K.

This formula is the basis for all forms of engines that transform heat into mechanical energy aka work. There exist other formulas for different machines but all of them produce a lower result than the maximum theoretical formula depicted above.

Let us look at a coal fired power plant

In a coal fired power plant you burn coal to boil water and add heat to the steam until it has a high pressure and then you release the steam through a turbine and the rotary motion of the turbine is directly used in an attached generator to “push the electrons through the grid”. You can today handle a steam temperature of about 600 degrees Celsius that is 873,15 K.

Now let us see what the efficiency will be when the waste heat goes into a nearby river at 10 degrees Celsius or 283,15 K:

eta = 1 – ( 283,15 K / 873,15 K ) = 0,675 that equals 67,5 %

Yes, this is the theoretical maximum thermal efficiency that you can obtain when you run a water heater and a turbine with the maximum temperature of 600 degrees Celsius and the minimum of 10 degrees Celsius. That is it! You can not obtain a higher (theoretical) efficiency at these temperatures. Actually the result you obtain from a modern real coal fired power plant is somewhere at 55%. That means from the energy that is in the coal we only get 55% as electricity!

Nuclear power plants actually work with the same technology, they boil water and heat steam to release it in a turbine. These also can never ever have an efficiency higher than 67%

. They actually have something like 45% efficiency but that does not matter as Uranium, the source of that power, seemed to be virtually unlimited compared to the amount of energy you could obtain from 1 kilogram of Uranium.

What can you do to increase the efficiency of a heat engine?

You can increase T2 or decrease T1. Lets look at the options:

a) decrease T1: actually you could run the plant in Antarctica where the temperature is say minus 30 degrees aka 243,15 K. You will obtain eta of 0,72 aka 72%

Nobody actually runs a power plant there but the reason why airplanes fly as high as possible (depending on the oxygen level) is that the turbine of the plane has a higher efficiency the colder it is outside.

b) you can not increase steam to much more than 600 degrees Celsius because the steel will become affected. What you can actually do is to run a combustion process inside a turbine and that will lead to gas temperatures of about 800 degrees Celsius and thus increases the eta to 0,736 aka 73,6%

A modern gas turbine has three advantages beyond a coal fired power plant:

. it has a higher overall efficiency and can reach 60% or even more

2. it can be activated from zero to 100% power in a few minutes whereas a coal fired plant or a nuclear plant can not be powered up and down so fast. That is an advantage for a grid with intermittent power supply from wind or solar.

3. You might read in the newspaper a message that the global usage of coal has gone down in the recent years and that should be a sign of applied climate protection. In reality what has happened is, that the gas prices went down globally and the efficiency for gas turbines is a bit higher so that many coal fired power plants have been converted to gas turbine power plants. You can see the effect when you look at all fossil fueled powered plants. The carbon footprint of humanity has again increased recently after being stable for a short period. We have increased our energy consumption with some higher efficiency. We see that current carbon dioxide emissions are on the rise again as the efficiency gains are all maxed out.

The very last point that we want to look at is the “addition” of efficiency factors.

Let’s assume, we want to convert a temporary oversupply of solar energy with our photovoltaic cell to electricity, from that electricity we want to create methane that we can store somewhere and use it at another time when we need electricity in a gas turbine to recreate the electricity for us.

We will use the following efficiency factors in the process:

The inverter from the PV module to create electricity that can be fed into the grid at an eta of 90%

The machine that creates the methane from the grid energy at an eta of 65%

The machine that compresses and stores the gas somewhere at an eta of 90%

The gas turbine that converts the methane back into electricity at an eta of 65%

How does this all add up? Actually combined efficiencies are not added but multiplied.

Let’s do the math:

eta “powertogas” = 0,9 * 0,65 * 0,9 * 0,65 = 0,34

So if we wanted to use the “power to gas” technology we would have an overall efficiency of 34%! We will loose 66% of the expensive PV energy that is quite rare when we want to use gas as intermediary storage. I do not think, we can make that process economically possible when the wholesale price for electrical energy is at 5ct/KWh (Eurocent per kilo Watt hour). We might add one or two percent of efficiency here or there and research is being done about it, but this will not be very economical.

Actually PV modules currently have a maximum efficiency of about 20%, the theoretical achievable efficiency is somewhere at 27% (convert light into electricity in a solid-state-material process).

As Intrenex says: The supply with renewable energy must always be complete with only a very modest usage of storage applied and that is hydro power plants that have an efficiency of 80%. for a cycle of pumping the water up and releasing it downwards later.

Now as we have the theoretical knowledge about energy and power, let’s go to the large numbers:

Greek abbreviations for large numbers (with exponent of 10)

1.000 = 10 ^3 : Kilo, k (small anomaly, Kilo is a lowercase k)

1.000.000 = 10^6: Mega, M = 10^9: Giga, G = 10^12 Tera, T = 10^15 Peta, P = 10^18 Exa, E

When you multiply two large numbers ths exponent of the factor 10^x adds up:

1 hour of work at the power of 1 kW = 1 kWh

1000 hours of work at the power of 1 kW = 1 MWh

1000 hours of work at the power of 1 MW = 1 GWh

1000 hours of work at the power of 1 GW = 1 TWh

One year has 365 d/a * 24 h/d = 8760 h/a (h = hour, d = day, a = year)

A regular coal fired power plant has a size between 400 MW and 1200 MW (large ones usually have several fire stations)

If we consider these to run at 100% (what is not possible as there exist maintenance intervals and the grid does not always request full power) we get the following numbers for the work we can do with that in one year:

400MW * 8760 h = 3,504 TWh

12000 MW * 8760h = 10,512 TWh

So a coal fired power plant can deliver somewhere between 3 and 10 TWh of electrical energy.

Now we look at nuclear power:

There currently exist about 475 nuclear power stations in the world. Their power output ranges from 1000 to 1200 MW, so we can fairly assume that we have about 1 GW of power from one nuclear power plant. Nuclear power plants have a fair amount of maintenance as we want to apply high security, so they run about 5000 hours a year.

475 GW * 5000h = 2,375 PWh possible work being done by nuclear power worldwide in one year.

Europe for example has an installed electrical power generation capacity of about 1200 GW. That equals to 1,2 TW. That includes all kinds of electrical power generation from renewables to nuclear.

What we really want to do is stop climate change and the main evil components here are coal fired power plants. They have a low efficiency and produce potentially the most CO2 per energy unit.

The global total capacity of coal fired power plants is 6600 GW, equaling 6,6 TW.

So our first goal is to replace 6,6 TW of coal fired power plants globally.

We must put this into perspective: As we have seen in the section about efficiency, not the total energy contained in the coal is being converted into electricity. This reflects the so called “primary energy”. Primary energy is the theoretically contained chemical energy in a fossil or nuclear fuel that we can obtain by fission or burning. Every item we use in our daily life contains some form of primary energy, be it in the form of oil for transportation included, be it in the form of natural gas that has been used to create fertilizer or be it in the form of coal or gas for heating and electricity.

The content of renewable energy is really negligible as renewable energy generation only supplies 2% of global energy consumption.

The total primary energy use goes directly into climate disruption. About 25% is the generation of electrical energy, 25% goes into the use in agriculture, 25% goes into the use of heating and cooling and 25% goes into the transportation sector.

Our goal to replace 6,6 TW of coal fired power plants for electrical energy creation only reflects 25% of the total primary energy usage. The other 75% going into other aspects of our economy are usually being left out by proponents of renewable energy as the energy form created by renewables is electricity.

Now we want to see, what we have to do if we start with coal fired power plants and build up 6,6 TW of renewable energy:

6,6 TW equals 6,6 Million MW : 6,6 TW = 6.600.000 MW = 6.600.000.000 kW.

Photovoltaics PV:

If we were not concerned about the price, we could use PV panels that generate 200W each. So to generate 1 kW of electrical power, we need 5 panels
. To generate 6,6 TW of electrical power would then require PV panels. Does this look like a big number?

If we are able to install 1 million panels in a year this would take 33.000 years. I bet you start to realize how big the task is, we are talking about…

Wind energy:

We again leave out problems with size and price and we assume that we can install wind turbines at a capacity of 5 MW each. This is the largest turbine available on the market, it has a tower height of about 150 m and a total height of about 200 m.

6,6 TW = 1.320.000 * 5 MW

So to build one of these gigantic machines, we might need one month. The installation of 1,32 million wind turbines globally would then take 1,32 million months aka 110.000 years.

We actually want to be finished with the task in 2050, so we really need a gigantic capacity of constructing all of this new machinery and it does not really matter, what form of renewable energy we use, the numbers just are really, really big.

Intrenex says: We must switch to renewables as soon as possible on a global scale but to reach that goal we must drastically reduce our energy needs. Otherwise, we will waste time and resources and our economic and biosphere capacity will be exhausted before we finish that task.

There does not exist a single civilization that avoided collapse because it voluntarily stopped increasing it’s resource usage or even reduced it. To claim that this time it will be different as we are geniuses today is a possibility but a very small one if we do not take very bold steps.

In the last section, we want to look at some aspects of our future and how we can reach a good one.

We know that there exists a large discrepancy in wealth distribution across all humans living on Earth. That includes energy usage distribution.

Some research has been done in Switzerland and the scientists came up with the statement that a living standard quite similar to the one used today in the OSCE countries was possible on the consumption of 2000 Watts per person.

This consumption level would be available for every human on the planet and include all forms of energy used in transportation, electricity, heating and cooling and agriculture, so 100% of all primary energy use.

If we sum this up, we can come to the conclusion that a renewable energy supply for 7,5 billion people would require the installation of 15 TW of renewable energy. If we add up losses and other factors, we can say that the final energy consumption on this planet should not be larger than three times the goal of replacing coal with 6 TW. This will be significantly lower than the total primary energy use today.

Unfortunately not every renewable installation runs for 100% of the time. When we do what Intrenex proposes to create a large supergrid to smooth out regional differences, the total installation base should be something like 10 – 25 % larger. 20 TW will possibly do the job.

This goal is possible but the task is really extraordinarily gigantic.

I hope you realize that we can not solve our climate and energy problem by installing some small PV systems on some wealthy private home roofs. We must take an action of enormous industrial dimensions and only the supergrid INTRENEX proposes has even a small chance of being realistic

. Get realistic and help us to do it.

Let love and reason guide us