Examples of the First Law of Thermodynamics, or the Conservation of Energy Law.

topExamples of the First Law of Thermodynamics, also known as the Conservation of Energy Law. Energy flow in diesel engine.
The Conversion of mechanical energy into heat. Examples of how thermal efficiency is defined.

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Examples of the First Law of Thermodynamics

Energy Flow in a Diesel Engine
When an engine burns fuel it converts the energy stored in the fuel's chemical bonds into useful mechanical work and into heat. Different types of fuel have different amounts of energy, but in any given gallon or liter of fuel there is a set amount of energy. That's all there is, there ain't no more. No magic devices or cow magnets strapped to the fuel line will change that.

The conservation of energy principle defined by the first law of thermodynamics says that when all of the fuel's energy is released by burning in the engine's cylinders it doesn't disappear. The total quantity of energy stays the same and must be accounted for. In the case of the diesel engine shown below it either becomes thermal energy (heat) or mechanical energy (work). For every 100 units of fuel energy that is burned in the engine a hundred units of converted energy has to end up somewhere. It doesn't disappear.

The picture below shows one example of where the energy goes. The example assumes the engine is operating in what we call "steady state".

Energy flows in a diesel engine obey the Laws of Thermodynamics.

If I did the numbers right, the sum of all the energy out will equal the sum of the energy into the engine. That's what the First Law of Thermodynamics predicts. If the numbers don't add up, it's due to human error, not a violation of the laws of physics.

			Can Energy Be Consumed? Sometimes people say energy is "consumed". They say something like, "That power plant consumes 80 bugazillion gaggledorks of energy each day". Okay, I never heard that exact example, take it as an analogy (And don't write and ask me what a gaggledork is!). These people are to be pittied, not condemned. (There's plenty of condemning already in the world.) They just haven't read this website yet. Unlike you, they don't understand about the first law of thermodynamics. You know by now that energy is never consumed. It doesn't go away. It is conserved. It is constant. It only changes or moves. At the end of every process or happening the total amount of energy is unchanged. It did not go away, dissappear, or change amount. It may have changed from chemical to kinetic energy, or electrical energy to thermal, but the total amount stayed the same. It was not consumed! But alas, something does sort of get consumed. That may not be quite the correct word. Something that we engineers call availabilty or exergy or just plain ol' usefulness. "Call me less useful," said Energy after it was converted. The exciting (okay, I'm a nerd) Second Law of Thermodynamics explores this concept. Energy does get less useful as it moves through its changes. Not to be explored in this section about the first law, but keep it in mind. You don't know the "rest of the story", until you understand this.

Notice that for every 100 units or "chunks" of fuel energy burned in the engine, only 41 units of useful energy are delivered to the shaft as rotating useful energy (thermal efficiency = 41%). That doesn't seem so great, does it? But that's actually very good. Most engines do less than 40 - some don't even make it into the 30's. And the old steam locomotives barely got 5 or 6 units of useful work out of 100 units of wood or coal energy (thermal efficiency of 5% or 6%) they burned. Things have improved.

As the drawing shows, more than half of the energy in the fuel leaves the engine as thermal energy, or "waste heat" as we mechanical engineers like to call it. In most engines 30 percent or more goes right out the exhaust stack in the hot exhaust gas. Friction heat from the parts in the engine rubbing together is absorbed by the engine oil which lubricates the rubbing surfaces to keep the parts from overheating and melting. The rest of the thermal energy flows into the cooling water through the engine cylinders mostly. If the engine has an aftercooler some of the thermal energy goes out there.

Engineers that design and build engines pay close attention to where the energy goes. We carefully measure the temperatures and flows of all the fluids into and out of the engine. This allows us to figure out exactly where the energy is going. What we want is to convert as much of the fuel's energy as possible into useful work. To do that we first have to know where the energy is going. Then we can try to figure out how to convert more into work and less into "waste heat".

Thanks to an understanding of the laws of thermodynamics, modern engines are significantly more efficient than they used to be. But as the second law of thermodynamics tells us, there is a limit to how efficient engines can be, and it is not very close to 100%. Some engines are getting close to the practical limits now. That subject will be covered more in the coming section on the 2nd Law.

Converting Work to Heat

	We take it for granted these days that work can be coverted into heat and heat into work. But this wasn't really understood by humans until fairly recently. The drawing on the right shows how an early experimenter was able to figure out how to compare mechanical energy to thermal energy. James Prescott Joule was his name. This simple experiment helped to change the world by helping us to understand the way energy really behaves.

The knowledge that mechanical work could be converted to heat and that we could measure and predict how much heat would result from a given amount of work was a huge discovery - a really big deal.

To show our appreciation we named a unit of energy after Mr. Joule. It's called, surprisingly enough, the Joule (J) and in the SI system of units it is equivalent to the mechanical units of work of 1 Newton (force) meter (length). 1 J = 1 N-m.

In the experiment Joule simply attached a weight by pulley and string to some paddles in an insulated container of water. The weight turns the paddles as it falls. The turning paddles do work on the water (they push it all around, "churning it up") equal to the force of gravity on the weight times the distance (L) the weight is pulled down by the gravitational force. It's the formula for work - force times distance. By the time the weight stops, all of it's potential energy at the start of the "fall" has been transferred by the work process into the water (minus a little friction in the pulley and ropes). What happened to the energy? If the first law of thermodynamics is true it had to end up somewhere, it couldn't just dissappear. Joule measured the water temperature and found the temperature had increased. Yup, the water was a little bit warmer because the mechanical work of the paddles had increased the energy level of the water molecules by pushing them around.

Through experiments like this, Joule and others, were able to determine the equivalent values of thermal energy and mechanical energy. This knowledge allows us to keep track of all the energy in complicated processes. For example, by knowing that a certain amount of work can be converted into a certain amount of heat, we are able to accurately account for all of the fuel's energy as it is converted in an engine, as shown in the example above. Amazingly enough when measured carefully and accurately, all of the energy out does equal the energy in. Really! I've done it.

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Digressions & Further Explanations Section

Energy Stored in Fuel
How much energy is stored in fuel? It depends on the fuel. There's all kinds of fuel. Diesel fuel, gasoline (or petrol as it's called in some countries), methanol in race cars, jet fuel in jets, propane in fork lifts and backyard grills, and some engines burn a gas called natural gas which is mostly made of methane.

It is fairly straight forward with a liquid fuel like diesel to measure the energy content in a sample. A little bit of the fuel is burned in something called a "bomb calorimeter" and the energy released by combustion is measured by the increase in temperature of a surrounding water bath that absorbs the energy.

This is generally called the Heating Value of the fuel. Fuels like diesel and gasoline actually vary quite a bit in composition being generally a hodge-podge of different hydrocarbon molecules. When measuring fuel consumption in an engine lab or doing an energy balance like the one shown in the picture above, it is very important to have an accurate heating value of the fuel being burned, so it is typical to take frequent samples, each of which are sent to the lab to be analyzed. If you don't have an accurate heating value then your value of fuel energy into the engine won't be accurate.

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"Energy In" Equals "Energy Out" plus "Energy Stored":
Steady State means the engine is running at a steady constant load and constant speed and is not warming up or cooling down. In this steady state condition the energy flows are also steady and constant.
Sometimes people say the conservation of energy is "Energy In" equals "Energy Out". This is only true for steady state systems. A good example is our engine above. If the engine has just been started after sitting all night and getting cold it will take a while to get warmed up before it reaches steady state. During the warm up period, some of the fuel's energy will go into heating up the cold metal and cold water. The engine's temperature control valves (thermostats) will keep the engine water from flowing to the radiator until it gets warm enough. If we measure the energy flowing out of the engine during the warm up period we would find that less energy is flowing out than is going in. Some energy is being stored in the engine parts and fluids. It is hard to measure this, but if you could you would find that the energy heating up the metal, oil, and water (stored energy), plus the energy flowing out in the oil, cooling water, and exhaust exactly equals the energy in the fuel going in.

Eventually all the fluids and engine parts will reach a constant operating temperature. Then we can say the engine is operating in steady state and the energy out equals the energy in.

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Thermal Efficiency
When people talk about the efficiency of an engine, they are usually describing what we engineer's call thermal efficiency. In the case of engines that burn fuel, this is simply the useful mechanical work out of the engine divided by the energy in the fuel burned. Since we know the conversion between mechanical and thermal energy (see thermal energy below) we can relate the thermal energy available in the fuel to the mechanical energy produced by the engine.

Of course, what we are really interested in is power which is how much energy is produced or used in a given amount of time. So when I say my engine is burning 100 units of energy every hour that is actually a measure of power (energy/time). If our engine has a thermal efficiency of 41% then it is producing 41 units of useful mechanical energy every hour. If we are buring 1000 units of fuel energy during the same hour that is 10 times the power. And if the engine burning 10 times the amount of energy every hour also has a thermal efficiency of 41% then it is producing 410 units of energy every hours (410/1000 = 0.41).

With engines like the diesel engine above, we generally define useful energy as the rotating energy delivered at the shaft coming out of the engine. The power produced here is called shaft power or brake power. The effiency then is called brake thermal efficiency. But we can measure the power anywhere we want to, as long as we clearly define it so as not to confuse anyone. For example, if the engine shaft is attached to an alternator we might measure the electricity produced by the alternator. If the alternator has an efficiency of 96% then the power out of the alternator will be 96% of the shaft power from the engine, and we would say the electrical efficiency is about 39%. This is painful, but fair, after all the useful energy to us in this case, is really the electricity coming out of the alternator, not the brake power from the engine going into the alternator.

But the reason we like to define the useful power at the same place on different engines is so that we can compare engines. If one engine has a brake thermal efficiency of 41% and another different engine has a brake thermal efficiency of 38% we know that the engine with the higher efficiency will be more fuel efficient. It will produce the same amount of power while burning less fuel. If you are the one paying for the fuel, you will appreciate that.

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Thermal Energy vs. Heat
If you've read my pages on energy types and heat flow, you know that most thermodynamics text books describe heat as an energy transfer process rather than a type of energy. The same goes for work. By this strict and nit-picky interpretation, work and heat are the two ways that energy can be changed or transferred. Thus they are processes of change rather than types of energy. This strictness is useful to help understand energy better, but I don't really lose sleep over it. It seems that most science books at the high school level and below describe both heat and work as types of energy, so most of the students and teachers visiting my pages are being taught heat and work are types of energy. Some college thermodynamics texts still do discuss heat as a form of energy, while others prefer the term thermal energy or internal energy. I was schooled with the term internal energy which is most descriptive since this type of energy is really made up of all the energies of the atoms and molecules inside a substance. But recently I've decided the term thermal energy is my favorite and so I've started to use it in this website. But, hey, I use all three terms interchangeably, so get used to it. If I just say heat I usually mean thermal energy. If I am describing the process of energy transfer I usually say "heat flow" or "heat flow process".
And if you read and understood all that, you deserve the "hand shake of honor", and maybe even an ice-cream cone.

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©Copyright 2005, 2017 David Watson. All rights reserved. Everything in the FT Exploring web site is copyrighted, either by us or by someone else. For information concerning use of this material, click on the word Copyright to go to our legal page.