Thermodynamics: Principles and Applications
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Thermodynamic laws
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By Saha
This is the natural continuation of my previous article entitled Thermodynamics: The Fundamentals. I will present the 4 major principles that are posed by the thermodynamics, which led to the understanding, construction and improvement of thermodynamic machines like the steam engine, the gasoline engine, the heat pump or air conditioner .
Zero Principle
It's called principle zero because it is this principle that allows the study of thermodynamics using the variable temperature. It can be expressed as follows:
"Temperature is a physical benchmarks to characterize the state of a system"
In other words: "You can make a thermometer". A body is said to be in thermal equilibrium if its temperature does not change over time. If 2 single body are in contact then they evolve to an equilibrium temperature where they will have the same temperature.
First principle
The first principle is the conservation of energy can be formulated as follows:
First principle
The first principle is the conservation of energy can be formulated as follows:
"During processing in a closed system, the variation of internal energy of the system is equal to the quantity of energy chang e with the external environment as heat and work"
We can then write mathematically as: where dU is the change of internal energy of the system, dQ is a small amount of heat given to the system and dW is a small amount of work received by the system.
Can be summarized this principle by the famous maxim: "Nothing is lost, nothing is created, everything is transformed" wrongly attributed to Antoine Lavoisier as the philosopher Anaxagoras of Presocrats ClazomÃ¨nes wrote to the 5th century BC that: "Nothing arises nor perishes, but already things are combined and then separate again. " We see that the concept of energy conservation is very old but the first law of thermodynamics states that the internal energy of a system (sum of the microscopic energy) may be modified by adding or removing heat and work .
Here we understand the value of this principle for the construction of thermal machines which have to convert heat into work (steam engine, engine, etc..) Or to transform the work into heat (heat pump, refrigerator, air conditioner, etc.)..
Second principle
This principle, formulated in 1865 by German physicist Rudolf Clausius, which introduces a new variable called entropy and rated 'S'. The second principle is stated as follows:
Can be summarized this principle by the famous maxim: "Nothing is lost, nothing is created, everything is transformed" wrongly attributed to Antoine Lavoisier as the philosopher Anaxagoras of Presocrats ClazomÃ¨nes wrote to the 5th century BC that: "Nothing arises nor perishes, but already things are combined and then separate again. " We see that the concept of energy conservation is very old but the first law of thermodynamics states that the internal energy of a system (sum of the microscopic energy) may be modified by adding or removing heat and work .
Here we understand the value of this principle for the construction of thermal machines which have to convert heat into work (steam engine, engine, etc..) Or to transform the work into heat (heat pump, refrigerator, air conditioner, etc.)..
Second principle
This principle, formulated in 1865 by German physicist Rudolf Clausius, which introduces a new variable called entropy and rated 'S'. The second principle is stated as follows:
"Any transformation generates the thermodynamic entropy"
The entropy is an extensive quantity and is defined as the change during a reversible transformation is equal to the amount of heat given to the system divided by the temperature of that system, see equation (1).
If the transformation is irreversible, then there is a creation of positive entropy due to dissipative phenomena (friction, diffusion, etc..), See equation (2). We can then deduce the famous inequality of Clausius, which summarizes the second principle and is represented in the inequality (3):
In fact, a reversible transformation is not perfect, all known real transformations are irreversible and will create entropy. The total entropy of the universe is in constant increase since its birth. This statement is very important in thermodynamics and many fell at the scientific level but also at the philosophical level.
For the construction of thermal machines, we must understand this principle that the entropy generation is a problem created because the entropy will decrease the future performance of the machines. That means making machines that minimize the creation of entropy, ie mainly to minimize friction losses. It naturally includes an engine that runs very quickly will have better performance if the friction is minimal.
Third principle
This principle, also known Nernst principle was enunciated in 1904:
If the transformation is irreversible, then there is a creation of positive entropy due to dissipative phenomena (friction, diffusion, etc..), See equation (2). We can then deduce the famous inequality of Clausius, which summarizes the second principle and is represented in the inequality (3):
In fact, a reversible transformation is not perfect, all known real transformations are irreversible and will create entropy. The total entropy of the universe is in constant increase since its birth. This statement is very important in thermodynamics and many fell at the scientific level but also at the philosophical level.
For the construction of thermal machines, we must understand this principle that the entropy generation is a problem created because the entropy will decrease the future performance of the machines. That means making machines that minimize the creation of entropy, ie mainly to minimize friction losses. It naturally includes an engine that runs very quickly will have better performance if the friction is minimal.
Third principle
This principle, also known Nernst principle was enunciated in 1904:
"If the temperature of a system tends to absolute zero, then the entropy tends to zero"
The foundations and implications of this principle, related to quantum physics are complex but did not affect the classical thermodynamics and the construction of thermal machines. I can therefore not go into details here.The thermal machines
A thermal machine can respond to 2 main functions:
- Transforming the Work in the heat (to move an object from heat): steam engine, heat engine (internal combustion engine, gasoline, diesel, alcohol or gas in cars, jet engines on airplanes) and so on.
- Transforming work into heat (from hot to cold or from a moving object): heat pump, refrigerator, air conditioner, etc..
The thermal machines are based on a set of thermodynamic transformations that one comes to subject a fluid and cyclical. In our study thermodynamics, fluid is then our system will come from the heat exchange and work with the external environment.
- In a steam engine, the fluid in question is the water that we usually just heat with a coal boiler to evaporate water (a pport heat). The steam then activates a piston that will lead to a wheel through a crankshaft and cause a rotational movement (job creation). Illustration of a steam engine (source: Wikipedia):
- For a motor car explosion, the fluid used is of the essence, diesel, alcohol or gas (LPG) by the motors. In a petrol engine 4 stroke classic, it comes to blow up a air / fuel mixture in a combustion chamber with a small spark foune by candles (heat). This explosion allows the movement of a Pison which will generate a rotary motion via a crankshaft to rotate the wheels (the creation of work). Illustration of a 4 stroke engine (source: Wikipedia):
- In refrigerators use a fluid called "refrigerent" as a heat transfer fluid (which carries the heat). Freon was used at the beginning but now they are complex fluids such as dichlorodifluoromethane, the tetrafluoroethane or methylpropan that are less harmful to the environment. The general principle of the refrigerator is to compress a fluid through a compressor (labor input) and then perform a relaxation (decrease fluid pressure suddenly) to the cold. Air conditioners are based on the same principle and heat pumps are just air conditioners that work 'in reverse'. A future note will be dedicated to refrigeration machines.
For convenience, we represent these transformations in diagrams that can be of various natures. One of the best known is the Clapeyron diagram that illustrates the evolution of pressure and volume of fluid during the transformation. Thus, each line between 2 points in the diagram corresponds to a processing performed by special equipment (heat exchanger, valve, turbine, piston ...) between 2 states of the fluid.
Carnot Cycle
the early 19 th century, Sadi Carnot, the famous physicist and french engineer, sets the ideal thermodynamic cycle to produce mechanical work from a heat source and a cold: The Carnot cycle. Carnot's research was vital in his time machine to produce steam optimal improving yields and it is also the first to express the scientific principle of heat engine in which all the engines are now built in cars and aircraft (engine explosion and jet engines).
This cycle is reversible, if taken in the opposite direction, there is also the ideal cycle to share the warmth of a hot spring in a cold source from a source of employment data. In other words: the ideal refrigeration cycle!
The Carnot cycle consists of a set of reversible adiabatic transformations 2 (no heat exchange with the outside entropy constant) and 2 transformations isotherms (constant temperature). In the direction of clockwise, it is a motor cycle and the transformations are:
- From 3 to 4: Isotherme compression Q1 where heat is extracted from the system to the cold source is at a temperature T1 (ie Q1 <0)>Reversible adiabatic (isentropic) Compression
- From 1 to 2: Isothermal heat addition where Q2 is given to the system via a source that is hot at the temperature T2 (ie Q2> 0)
- From 2 to 3: Reversible adiabatic (isentropic) expansion The Carnot engine cycle in the Clapeyron diagram (according to the Pressure Volume)
In total, this cycle produces a mechanical work W = Q1 + Q2 and a quantity of heat Q1 for a given quantity of heat equal to Q2, and this is the best cycle between a hot and a cold source.
If we apply the 2nd law of thermodynamics in this cycle by saying that it is ideal (adiabatic reversible transformation, thus constant entropy), we can make a balance of entropic cycle.
- During the transformation from A to B, the entropy extracted from the system is equal to the amount of heat Q1 negative divided by T1, see equation (1)
- During the conversion of C to D, the entropy provided to the system is equal to the amount of heat Q2 positive divided by the temperature of processing, or T2, see equation (2)
- The other 2 changes are therefore reversible adiabatic transformations entropy remains constant. We can therefore say that the entropy lost between A and B is equal to the entropy gained between C and D, see equation (3) represents the equation of Clausius-Carnot and defines the necessary heat exchange between a hot source (at temperature T2) and source cold (at temperature T1).
Example of Carnot cycle
It is considered a kind of ideal steam engine that uses water as a fluid and which is based on a Carnot cycle (impossible to achieve). In our hypothetical machine, the cold source is at room temperature, ie T1 = 20 ° C = 293 kelvin. The heat is the temperature of the water vapor that is T2 = 100 ° C = 373 kelvin. If we make a quantity of heat Q2 = 500 watt, then the amount of heat is extracted from the system according to the equation of Clausius-Carnot equal to Q1 = - T1 * (Q2/T2) = - 293 * (500/373) = -393 Watt. The work provides is equal to W = Q1 + Q2 = 500 - 393 = 107 Watt.
This means that between 20 ° C and 100 ° C, if we make a quantity of heat of 500 watts, we can extract the best of cases a mechanical power of 107 watts, peak performance is W/Q2 n = = 107/500 = 21%. Physics teaches us that it is impossible to manufacture a machine with a thermal efficiency greater than 21% between 20 ° C and 100 ° C. More generally it can be shown that the performance for a Carnot engine depends only on warm and cold temperatures and that this return is equal to:
All thermodynamic machines trying to get closer to the Carnot cycle but it is unattainable in part because the second law of thermodynamics which states that any transformation generates entropy. Transformations isentropic (reversible adiabatic) are impossible, as well as isothermal compressions because when a gas compresses, it just generates heat due to friction, which has the effect of increasing the temperature of the system.
For example, a gasoline combustion engine operates between 20 ° C (293 K) and 500 ° C (773 K) around its Carnot efficiency is therefore 1-273/773 = 62%. In fact, a gasoline engine has an efficiency of about 36% in operation and 15% in degraded operation (eg in town) because of the generation of entropy in the various transformations and the generation of heat of compression.
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