Statistical Mechanics
Statistical mechanics is the application of probability theory, which includes mathematical tools for dealing with large populations, to the field of mechanics, which is concerned with the motion of particles or objects when subjected to a force. Statistical mechanics, sometimes called statistical physics, can be viewed as a subfield of physics and chemistry.
It provides a framework for relating the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials that can be observed in everyday life, therefore explaining thermodynamics as a natural result of statistics and mechanics (classical and quantum) at the microscopic level. In particular, it can be used to calculate the thermodynamic properties of bulk materials from the spectroscopic data of individual molecules.
This ability to make macroscopic predictions based on microscopic properties is the main advantage of statistical mechanics over thermodynamics. Both theories are governed by the second law of thermodynamics through the medium of entropy. However, entropy in thermodynamics can only be known empirically, whereas in statistical mechanics, it is a function of the distribution of the system on its micro-states.
Kinetic Theory
Kinetic theory (or kinetic theory of gases) attempts to explain macroscopic properties of gases, such as pressure, temperature, or volume, by considering their molecular composition and motion. Essentially, the theory posits that pressure is due not to static repulsion between molecules, as was Isaac Newton's idea, but due to collisions between molecules moving at different velocities. Kinetic theory is also known as the kinetic-molecular theory or the collision theory.
The theory for ideal gases makes the following assumptions:
The gas consists of very small particles, each of which has a mass or weight in SI units, kilograms.
The number of molecules is large such that statistical treatment can be applied.
These molecules are in constant, random motion. The rapidly moving particles constantly collide with each other and with the walls of the container.
The collisions of gas particles with the walls of the container holding them are perfectly elastic.
The interactions among molecules are negligible. They exert no forces on one another except during collisions.
The total volume of the individual gas molecules added up is negligible compared to the volume of the container. This is equivalent to stating that the average distance separating the gas particles is relatively large compared to their size.
The molecules are perfectly spherical in shape, and elastic in nature.
The average kinetic energy of the gas particles depends only on the temperature of the system.
Relativistic effects are negligible.
Quantum-mechanical effects are negligible. This means that the inter-particle distance is much larger than the thermal de Broglie wavelength and the molecules can be treated as classical objects.
The time during collision of molecule with the container's wall is negligible as comparable to the time between successive collisions.
The equations of motion of the molecules are time-reversible.
Sunday, August 10, 2008
Friday, August 08, 2008
Thermodynamics---Lesson 5
Thermodynamic Processes
A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant. The pressure-volume conjugate pair is concerned with the transfer of mechanical or dynamic energy as the result of work.
An isobaric process occurs at constant pressure. An example would be to have a movable piston in a cylinder, so that the pressure inside the cylinder is always at atmospheric pressure, although it is isolated from the atmosphere. In other words, the system is dynamically connected, by a movable boundary, to a constant-pressure reservoir.
An isochoric process is one in which the volume is held constant, meaning that the work done by the system will be zero. It follows that, for the simple system of two dimensions, any heat energy transferred to the system externally will be absorbed as internal energy. An isochoric process is also known as an isometric process or an isovolumetric process. An example would be to place a closed tin can containing only air into a fire. To a first approximation, the can will not expand, and the only change will be that the gas gains internal energy, as evidenced by its increase in temperature and pressure. Mathematically, δQ = dU. We may say that the system is dynamically insulated, by a rigid boundary, from the environment.
An isothermal process occurs at a constant temperature. An example would be to have a system immersed in a large constant-temperature bath. Any work energy performed by the system will be lost to the bath, but its temperature will remain constant. In other words, the system is thermally connected, by a thermally conductive boundary to a constant-temperature reservoir.
An adiabatic process is a process in which there is no energy added or subtracted from the system by heating or cooling. For a reversible process, this is identical to an isentropic process. We may say that the system is thermally insulated from its environment and that its boundary is a thermal insulator. If a system has an entropy which has not yet reached its maximum equilibrium value, the entropy will increase even though the system is thermally insulated.
An isentropic process occurs at a constant entropy. For a reversible process this is identical to an adiabatic process. If a system has an entropy which has not yet reached its maximum equilibrium value, a process of cooling may be required to maintain that value of entropy.
Any of the thermodynamic potentials may be held constant during a process. For example:
An isenthalpic process introduces no change in enthalpy in the system.
A thermodynamic process may be defined as the energetic evolution of a thermodynamic system proceeding from an initial state to a final state. Paths through the space of thermodynamic variables are often specified by holding certain thermodynamic variables constant. The pressure-volume conjugate pair is concerned with the transfer of mechanical or dynamic energy as the result of work.
An isobaric process occurs at constant pressure. An example would be to have a movable piston in a cylinder, so that the pressure inside the cylinder is always at atmospheric pressure, although it is isolated from the atmosphere. In other words, the system is dynamically connected, by a movable boundary, to a constant-pressure reservoir.
An isochoric process is one in which the volume is held constant, meaning that the work done by the system will be zero. It follows that, for the simple system of two dimensions, any heat energy transferred to the system externally will be absorbed as internal energy. An isochoric process is also known as an isometric process or an isovolumetric process. An example would be to place a closed tin can containing only air into a fire. To a first approximation, the can will not expand, and the only change will be that the gas gains internal energy, as evidenced by its increase in temperature and pressure. Mathematically, δQ = dU. We may say that the system is dynamically insulated, by a rigid boundary, from the environment.
An isothermal process occurs at a constant temperature. An example would be to have a system immersed in a large constant-temperature bath. Any work energy performed by the system will be lost to the bath, but its temperature will remain constant. In other words, the system is thermally connected, by a thermally conductive boundary to a constant-temperature reservoir.
An adiabatic process is a process in which there is no energy added or subtracted from the system by heating or cooling. For a reversible process, this is identical to an isentropic process. We may say that the system is thermally insulated from its environment and that its boundary is a thermal insulator. If a system has an entropy which has not yet reached its maximum equilibrium value, the entropy will increase even though the system is thermally insulated.
An isentropic process occurs at a constant entropy. For a reversible process this is identical to an adiabatic process. If a system has an entropy which has not yet reached its maximum equilibrium value, a process of cooling may be required to maintain that value of entropy.
Any of the thermodynamic potentials may be held constant during a process. For example:
An isenthalpic process introduces no change in enthalpy in the system.
Thursday, August 07, 2008
Thermodynamics---Lesson 4
Statistical Thermodynamics
In thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of thermodynamic systems using probability theory. Statistical thermodynamics, generally, provides a molecular level interpretation of thermodynamic quantities such as work, heat, free energy, and entropy. Statistical thermodynamics was born in 1870 with the work of Austrian physicist Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.
Boltzmann's original papers on the statistical interpretation of thermodynamics occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. The term "statistical thermodynamics" was proposed for use by the American thermodynamicist Willard Gibbs in 1902. According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish
Classical thermodynamics vs. statistical thermodynamics
As an example, from a classical thermodynamics point of view we might ask what is it about a thermodynamic system of gas molecules, such as ammonia NH3, that determines the free energy characteristic of that compound? Classical thermodynamics does not provide the answer. If, for example, we were given spectroscopic data, of this body of gas molecules, such as bond length, bond angle, bond rotation, and flexibility of the bonds in NH3 we should see that the free energy could not be other than it is. To prove this true, we need to bridge the gap between the microscopic realm of atoms and molecules and the macroscopic realm of classical thermodynamics. From physics, statistical mechanics provides such a bridge by teaching us how to conceive of a thermodynamic system as an assembly of units. More specifically, it demonstrates how the thermodynamic parameters of a system, such as temperature and pressure, are interpretable in terms of the parameters descriptive of such constituent atoms and molecules.
In a bounded system, the crucial characteristic of these microscopic units is that their energies are quantized. That is, where the energies accessible to a macroscopic system form a virtual continuum of possibilities, the energies open to any of its submicroscopic components are limited to a discontinuous set of alternatives associated with integral values of some quantum number.
Chemical Thermodynamics
In thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of heat and work with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics. Chemical thermodynamics can be generally thought of as the application of mathematical methods to the study of chemical questions and is concerned with the spontaneity of processes.
The structure of chemical thermodynamics is based on the first two laws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.
The primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation. In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes:
Chemical reactions
Phase changes
The formation of solutions
The following state functions are of primary concern in chemical thermodynamics:
Internal energy (U)
Enthalpy (H).
Entropy (S)
Gibbs free energy (G)
Most identities in chemical thermodynamics arise from application of the first and second laws of thermodynamics, particularly the law of conservation of energy, to these state functions.
In thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of thermodynamic systems using probability theory. Statistical thermodynamics, generally, provides a molecular level interpretation of thermodynamic quantities such as work, heat, free energy, and entropy. Statistical thermodynamics was born in 1870 with the work of Austrian physicist Ludwig Boltzmann, much of which was collectively published in Boltzmann's 1896 Lectures on Gas Theory.
Boltzmann's original papers on the statistical interpretation of thermodynamics occupy about 2,000 pages in the proceedings of the Vienna Academy and other societies. The term "statistical thermodynamics" was proposed for use by the American thermodynamicist Willard Gibbs in 1902. According to Gibbs, the term "statistical", in the context of mechanics, i.e. statistical mechanics, was first used by the Scottish
Classical thermodynamics vs. statistical thermodynamics
As an example, from a classical thermodynamics point of view we might ask what is it about a thermodynamic system of gas molecules, such as ammonia NH3, that determines the free energy characteristic of that compound? Classical thermodynamics does not provide the answer. If, for example, we were given spectroscopic data, of this body of gas molecules, such as bond length, bond angle, bond rotation, and flexibility of the bonds in NH3 we should see that the free energy could not be other than it is. To prove this true, we need to bridge the gap between the microscopic realm of atoms and molecules and the macroscopic realm of classical thermodynamics. From physics, statistical mechanics provides such a bridge by teaching us how to conceive of a thermodynamic system as an assembly of units. More specifically, it demonstrates how the thermodynamic parameters of a system, such as temperature and pressure, are interpretable in terms of the parameters descriptive of such constituent atoms and molecules.
In a bounded system, the crucial characteristic of these microscopic units is that their energies are quantized. That is, where the energies accessible to a macroscopic system form a virtual continuum of possibilities, the energies open to any of its submicroscopic components are limited to a discontinuous set of alternatives associated with integral values of some quantum number.
Chemical Thermodynamics
In thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of heat and work with chemical reactions or with a physical change of state within the confines of the laws of thermodynamics. Chemical thermodynamics can be generally thought of as the application of mathematical methods to the study of chemical questions and is concerned with the spontaneity of processes.
The structure of chemical thermodynamics is based on the first two laws of thermodynamics. Starting from the first and second laws of thermodynamics, four equations called the "fundamental equations of Gibbs" can be derived. From these four, a multitude of equations, relating the thermodynamic properties of the thermodynamic system can be derived using relatively simple mathematics. This outlines the mathematical framework of chemical thermodynamics.
The primary objective of chemical thermodynamics is the establishment of a criterion for the determination of the feasibility or spontaneity of a given transformation. In this manner, chemical thermodynamics is typically used to predict the energy exchanges that occur in the following processes:
Chemical reactions
Phase changes
The formation of solutions
The following state functions are of primary concern in chemical thermodynamics:
Internal energy (U)
Enthalpy (H).
Entropy (S)
Gibbs free energy (G)
Most identities in chemical thermodynamics arise from application of the first and second laws of thermodynamics, particularly the law of conservation of energy, to these state functions.
Wednesday, August 06, 2008
Thermodynamics---Lesson 3
Thermodynamic Potentials
A thermodynamic potential is a scalar potential function used to represent the thermodynamic state of a system. One main thermodynamic potential which has a physical interpretation is the internal energy, U. It is the energy of configuration of a given system of conservative forces (that is why it is a potential) and only has meaning with respect to a defined set of references (or datums). In thermodynamics, certain forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mt. Everest than it would at the bottom of a the gravitational potential energy term in the formula for the internal energy would usually be ignored because changes in gravitational potential within the engine during operation would be negligible. Four common thermodynamic energy potentials are: Internal Energy, Entropy, Enthalpy, Gibbs Free Energy.
Internal Energy
Internal energy is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale. For example, a room temperature glass of water sitting on a table has no apparent energy, either potential or kinetic . But on the microscopic scale it is a seething mass of high speed molecules traveling at hundreds of meters per second. If the water were tossed across the room, this microscopic energy would not necessarily be changed when we superimpose an ordered large scale motion on the water as a whole.
Entropy
In thermodynamics entropy is a measure of the unavailability of a system’s energy to do work. It is a measure of the randomness of molecules in a system and is central to the second law of thermodynamics and the fundamental thermodynamic relation, which deal with physical processes and whether they occur spontaneously. Spontaneous changes, in isolated systems, occur with an increase in entropy. Spontaneous changes tend to smooth out differences in temperature, pressure, density, and chemical potential that may exist in a system, and entropy is thus a measure of how far this smoothing-out process has progressed.
When a system's energy is defined as the sum of its "useful" energy, (e.g. that used to push a piston), and its "useless energy", i.e. that energy which cannot be used for external work, then entropy may be (most concretely) visualized as the "scrap" or "useless" energy whose energetic prevalence over the total energy of a system is directly proportional to the absolute temperature of the considered system. Entropy is a function of a quantity of heat which shows the possibility of conversion of that heat into work. The increase in entropy is small when heat is added at high temperature and is greater when heat is added at lower temperature. Thus for maximum entropy there is minimum availability for conversion into work and for minimum entropy there is maximum availability for conversion into work. Entropy is one of the factors that determines the free energy of the system. This thermodynamic definition of entropy is only valid for a system in equilibrium (because temperature is defined only for a system in equilibrium), while the statistical definition of entropy (see below) applies to any system. Thus the statistical definition is usually considered the fundamental definition of entropy.
Entropy increase has often been defined as a change to a more disordered state at a molecular level. In recent years, entropy has been interpreted in terms of the "dispersal" of energy. Entropy is an extensive state function that accounts for the effects of irreversibility in thermodynamic systems. In terms of statistical mechanics, the entropy describes the number of the possible microscopic configurations of the system. The statistical definition of entropy is the more fundamental definition, from which all other definitions and all properties of entropy follow.
Enthalpy
In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H, h, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work obtainable from a closed thermodynamic system under constant pressure and entropy.
In terms of thermodynamics, enthalpy can be calculated by determining the requirements for creating a system from "nothingness"; the mechanical work required, pV differs, based upon the constancy of conditions present at the creation of the thermodynamic system.
Internal energy, U, must be supplied to remove particles from a surrounding in order to allow space for the creation of a system, providing that environmental variables, such as pressure (p) remain constant. This internal energy also includes the energy required for activation and the breaking of bonded compounds into gases.
This process is calculated as U + pV, to label the amount of energy or work required to "set aside space for" and "create" the system; describing the work done by both the reaction or formation of systems, and the surroundings. For systems at constant pressure, the change in enthalpy is the heat received by the system plus the non-mechanical work that has been done.
Therefore, the change in enthalpy can be devised or represented without the need for compressive or expansive mechanics; for a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.
The term pV is the work required to displace the surrounding atmosphere in order to vacate the space to be occupied by the system.
Gibbs Free Energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. Technically, the Gibbs free energy is the maximum amount of non-expansion work which can be extracted from a closed system or this maximum can be attained only in a completely reversible process. When a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy ΔG equals the work exchanged by the system with its surroundings, less the work of the pressure forces, during a reversible transformation of the system from the same initial state to the same final state.
The Gibbs free energy, originally called available energy, was developed in the 1870s by the American mathematical physicist Willard Gibbs. In 1873, in a footnote, Gibbs defined what he called the “available energy” of a body as such:
"The greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition."
The initial state of the body, according to Gibbs, is supposed to be such that "the body can be made to pass from it to states of dissipated energy by reversible processes". In his 1876 magnum opus On the Equilibrium of Heterogeneous Substances, a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical free energy in full.
In a simple manner, with respect to STP reacting systems, a general rule of thumb is:
"Every system seeks to achieve a minimum of free energy."
Hence, out of this general natural tendency, a quantitative measure as to how near or far a potential reaction is from this minimum is when the calculated energetics of the process indicate that the change in Gibbs free energy ΔG is negative. Essentially, this means that such a reaction will be favored and will release energy. The energy released equals the maximum amount of work that can be performed as a result of the chemical reaction. Conversely, if conditions indicated a positive ΔG, then energy--in the form of work--would have to be added to the reacting system to make the reaction go.
A thermodynamic potential is a scalar potential function used to represent the thermodynamic state of a system. One main thermodynamic potential which has a physical interpretation is the internal energy, U. It is the energy of configuration of a given system of conservative forces (that is why it is a potential) and only has meaning with respect to a defined set of references (or datums). In thermodynamics, certain forces, such as gravity, are typically disregarded when formulating expressions for potentials. For example, while all the working fluid in a steam engine may have higher energy due to gravity while sitting on top of Mt. Everest than it would at the bottom of a the gravitational potential energy term in the formula for the internal energy would usually be ignored because changes in gravitational potential within the engine during operation would be negligible. Four common thermodynamic energy potentials are: Internal Energy, Entropy, Enthalpy, Gibbs Free Energy.
Internal Energy
Internal energy is defined as the energy associated with the random, disordered motion of molecules. It is separated in scale from the macroscopic ordered energy associated with moving objects; it refers to the invisible microscopic energy on the atomic and molecular scale. For example, a room temperature glass of water sitting on a table has no apparent energy, either potential or kinetic . But on the microscopic scale it is a seething mass of high speed molecules traveling at hundreds of meters per second. If the water were tossed across the room, this microscopic energy would not necessarily be changed when we superimpose an ordered large scale motion on the water as a whole.
Entropy
In thermodynamics entropy is a measure of the unavailability of a system’s energy to do work. It is a measure of the randomness of molecules in a system and is central to the second law of thermodynamics and the fundamental thermodynamic relation, which deal with physical processes and whether they occur spontaneously. Spontaneous changes, in isolated systems, occur with an increase in entropy. Spontaneous changes tend to smooth out differences in temperature, pressure, density, and chemical potential that may exist in a system, and entropy is thus a measure of how far this smoothing-out process has progressed.
When a system's energy is defined as the sum of its "useful" energy, (e.g. that used to push a piston), and its "useless energy", i.e. that energy which cannot be used for external work, then entropy may be (most concretely) visualized as the "scrap" or "useless" energy whose energetic prevalence over the total energy of a system is directly proportional to the absolute temperature of the considered system. Entropy is a function of a quantity of heat which shows the possibility of conversion of that heat into work. The increase in entropy is small when heat is added at high temperature and is greater when heat is added at lower temperature. Thus for maximum entropy there is minimum availability for conversion into work and for minimum entropy there is maximum availability for conversion into work. Entropy is one of the factors that determines the free energy of the system. This thermodynamic definition of entropy is only valid for a system in equilibrium (because temperature is defined only for a system in equilibrium), while the statistical definition of entropy (see below) applies to any system. Thus the statistical definition is usually considered the fundamental definition of entropy.
Entropy increase has often been defined as a change to a more disordered state at a molecular level. In recent years, entropy has been interpreted in terms of the "dispersal" of energy. Entropy is an extensive state function that accounts for the effects of irreversibility in thermodynamic systems. In terms of statistical mechanics, the entropy describes the number of the possible microscopic configurations of the system. The statistical definition of entropy is the more fundamental definition, from which all other definitions and all properties of entropy follow.
Enthalpy
In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H, h, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the "useful" work obtainable from a closed thermodynamic system under constant pressure and entropy.
In terms of thermodynamics, enthalpy can be calculated by determining the requirements for creating a system from "nothingness"; the mechanical work required, pV differs, based upon the constancy of conditions present at the creation of the thermodynamic system.
Internal energy, U, must be supplied to remove particles from a surrounding in order to allow space for the creation of a system, providing that environmental variables, such as pressure (p) remain constant. This internal energy also includes the energy required for activation and the breaking of bonded compounds into gases.
This process is calculated as U + pV, to label the amount of energy or work required to "set aside space for" and "create" the system; describing the work done by both the reaction or formation of systems, and the surroundings. For systems at constant pressure, the change in enthalpy is the heat received by the system plus the non-mechanical work that has been done.
Therefore, the change in enthalpy can be devised or represented without the need for compressive or expansive mechanics; for a simple system, with a constant number of particles, the difference in enthalpy is the maximum amount of thermal energy derivable from a thermodynamic process in which the pressure is held constant.
The term pV is the work required to displace the surrounding atmosphere in order to vacate the space to be occupied by the system.
Gibbs Free Energy
In thermodynamics, the Gibbs free energy is a thermodynamic potential which measures the "useful" or process-initiating work obtainable from an isothermal, isobaric thermodynamic system. Technically, the Gibbs free energy is the maximum amount of non-expansion work which can be extracted from a closed system or this maximum can be attained only in a completely reversible process. When a system changes from a well-defined initial state to a well-defined final state, the Gibbs free energy ΔG equals the work exchanged by the system with its surroundings, less the work of the pressure forces, during a reversible transformation of the system from the same initial state to the same final state.
The Gibbs free energy, originally called available energy, was developed in the 1870s by the American mathematical physicist Willard Gibbs. In 1873, in a footnote, Gibbs defined what he called the “available energy” of a body as such:
"The greatest amount of mechanical work which can be obtained from a given quantity of a certain substance in a given initial state, without increasing its total volume or allowing heat to pass to or from external bodies, except such as at the close of the processes are left in their initial condition."
The initial state of the body, according to Gibbs, is supposed to be such that "the body can be made to pass from it to states of dissipated energy by reversible processes". In his 1876 magnum opus On the Equilibrium of Heterogeneous Substances, a graphical analysis of multi-phase chemical systems, he engaged his thoughts on chemical free energy in full.
In a simple manner, with respect to STP reacting systems, a general rule of thumb is:
"Every system seeks to achieve a minimum of free energy."
Hence, out of this general natural tendency, a quantitative measure as to how near or far a potential reaction is from this minimum is when the calculated energetics of the process indicate that the change in Gibbs free energy ΔG is negative. Essentially, this means that such a reaction will be favored and will release energy. The energy released equals the maximum amount of work that can be performed as a result of the chemical reaction. Conversely, if conditions indicated a positive ΔG, then energy--in the form of work--would have to be added to the reacting system to make the reaction go.
Thermodynamics---Lesson 2
Laws of Thermodynamics
If two thermodynamic systems are each in thermal equilibrium with a third, then they are in thermal equilibrium with each other.
When two systems are put in contact with each other, there will be a net exchange of energy between them unless or until they are in thermal equilibrium, that is, they contain the same amount of thermal energy for a given volume (say, 1 cubic centimeter, or 1 cubic inch.) While this is a fundamental concept of thermodynamics, the need to state it explicitly as a law was not perceived until the first third of the 20th century, long after the first three laws were already widely in use, hence the zero numbering. The Zeroth Law asserts that thermal equilibrium, viewed as a binary relation, is an equivalence relation.
First law of thermodynamics
In any process, the total energy of the universe remains the same.
It can also be defined as:
for a thermodynamic cycle the sum of net heat supplied to the system and the net work done by the system is equal to zero.
More simply, the First Law states that energy cannot be created or destroyed; rather, the amount of energy lost in a steady state process cannot be greater than the amount of energy gained.
This is the statement of conservation of energy for a thermodynamic system. It refers to the two ways that a closed system transfers energy to and from its surroundings - by the process of heating (or cooling) and the process of mechanical work. The rate of gain or loss in the stored energy of a system is determined by the rates of these two processes. In open systems, the flow of matter is another energy transfer mechanism, and extra terms must be included in the expression of the first law.
The First Law clarifies the nature of energy. It is a stored quantity which is independent of any particular process path, i.e., it is independent of the system history. If a system undergoes a thermodynamic cycle, whether it becomes warmer, cooler, larger, or smaller, then it will have the same amount of energy each time it returns to a particular state. Mathematically speaking, energy is a state function and infinitesimal changes in the energy are exact differentials.
Second law of thermodynamics
The entropy of an isolated system not in equilibrium will tend to increase over time, approaching a maximum value at equilibrium.
In a simple manner, the second law states that "energy systems have a tendency to increase their entropy" rather than decrease it.
A way of looking at the second law for non-scientists is to look at entropy as a measure of chaos. So, for example, a broken cup has less order and more chaos than an intact one. Likewise, solid crystals, the most organized form of matter, have very low entropy values; and gases, which are highly disorganized, have high entropy values. The entropy of a thermally isolated macroscopic system never decreases. However, a microscopic system may exhibit fluctuations of entropy opposite to that dictated by the Second Law. In a logical sense the Second Law thus ceases to be a "Law" of physics and instead becomes a theorem which is valid for large systems or long times.
Third law of thermodynamics
As temperature approaches absolute zero, the entropy of a system approaches a constant minimum.
In brief, this postulates that entropy is temperature dependent and leads to the formulation of the idea of absolute zero.
Stop This Biofuel Nonsense !!!!! ---summary/excerpt
In the Amazon, there is a land rush, accelerated by the most unlikely source – biofuels. An explosion of demand for farm-grown fuels has raised global food prices to a record high.
Propelled by mounting environmental concerns, biofuels has become the trendy way for politicians and corporations to show that they are serious about finding alternative sources of energy and in the process slow global warming.
Biofuels has done the opposite.
By diverting grain and oilseed crops from dinner plates to fuel tanks, biofuels are jacking up the world’s food prices, and endangering the hungry. The grain it takes to fill up the tank of 1 SUV can be used to feed a person for 365 days. Harvest are being plucked to feed our cars instead of our stomachs, and the U.N. declared it was a global emergency. Soaring corn prices has sparked tortilla riots in Mexico, flour prices have destabilized Pakistan, which was not exactly tranquil when flour was affordable.
Researchers have ignored the amazingly simple problem with biofuels, that using land to grow fuels lead to the destruction of forests, wetland, and grasslands that store enormous amounts of carbon. U.S. farmers are selling one-fifth of their corn to ethanol production, so U.S. soybean farmers are switching to corn, so Brazilian soybean farmers are expanding into cattle pastures, so Brazilian cattlemen are dispatched to the Amazon, where they clear new grazing lands in the Amazon rainforest or the Cerrado savanna, releasing vast amounts of carbon. In fact, only sugarcane based ethanol is efficient enough to cut emissions by more than it takes to produce the fuel, the rest of the ‘green’ fuels are net carbon emitters. U.S. leads the world in corn and soybean production, but even if 100% of its crop are turned into fuel, it would be only enough to offset just 20% of on-road fuel consumption.
The price of soybeans goes up, an the forests go down.
Propelled by mounting environmental concerns, biofuels has become the trendy way for politicians and corporations to show that they are serious about finding alternative sources of energy and in the process slow global warming.
Biofuels has done the opposite.
By diverting grain and oilseed crops from dinner plates to fuel tanks, biofuels are jacking up the world’s food prices, and endangering the hungry. The grain it takes to fill up the tank of 1 SUV can be used to feed a person for 365 days. Harvest are being plucked to feed our cars instead of our stomachs, and the U.N. declared it was a global emergency. Soaring corn prices has sparked tortilla riots in Mexico, flour prices have destabilized Pakistan, which was not exactly tranquil when flour was affordable.
Researchers have ignored the amazingly simple problem with biofuels, that using land to grow fuels lead to the destruction of forests, wetland, and grasslands that store enormous amounts of carbon. U.S. farmers are selling one-fifth of their corn to ethanol production, so U.S. soybean farmers are switching to corn, so Brazilian soybean farmers are expanding into cattle pastures, so Brazilian cattlemen are dispatched to the Amazon, where they clear new grazing lands in the Amazon rainforest or the Cerrado savanna, releasing vast amounts of carbon. In fact, only sugarcane based ethanol is efficient enough to cut emissions by more than it takes to produce the fuel, the rest of the ‘green’ fuels are net carbon emitters. U.S. leads the world in corn and soybean production, but even if 100% of its crop are turned into fuel, it would be only enough to offset just 20% of on-road fuel consumption.
The price of soybeans goes up, an the forests go down.
Tuesday, August 05, 2008
Thermodynamics
I will post a series of 9 lessons on thermodynamics. as follows:
Lesson 1: Heat and Temperature
Lesson 2: Laws of Thermodynamics
Lesson 3: Thermodynamic Potentials (Entropy, Enthalpy, Internal Energy, Gibbs Free Energy)
Lesson 4: Statistical Thermodynamics and Chemical Thermodynamics
Lesson 5: Thermodynamic Processes
Lesson 6: Thermodynamic Expansion
Lesson 7: Phase Changes
Lesson 8: Statistical Mechanics
Lesson 9: Kinetic Theory
Lesson 1: Heat and Temperature
Lesson 2: Laws of Thermodynamics
Lesson 3: Thermodynamic Potentials (Entropy, Enthalpy, Internal Energy, Gibbs Free Energy)
Lesson 4: Statistical Thermodynamics and Chemical Thermodynamics
Lesson 5: Thermodynamic Processes
Lesson 6: Thermodynamic Expansion
Lesson 7: Phase Changes
Lesson 8: Statistical Mechanics
Lesson 9: Kinetic Theory
Physics-Thermodynamics, Lesson 1
Heat
Heat may be defined as energy in transit from a high temperature object to a lower temperature object. An object does not possess "heat"; the appropriate term for the microscopic energy in an object is internal energy. The internal energy may be increased by transferring energy to the object from a higher temperature (hotter) object - this is properly called heating.
Temperature
A convenient operational definition of temperature is that it is a measure of the average translational kinetic energy associated with the disordered microscopic motion of atoms and molecules. The flow of heat is from a high temperature region toward a lower temperature region. The details of the relationship to molecular motion are described in kinetic theory. The temperature defined from kinetic theory is called the kinetic temperature. Temperature is not directly proportional to internal energy since temperature measures only the kinetic energy part of the internal energy, so two objects with the same temperature do not in general have the same internal energy (see water-metal example). Temperatures are measured in one of the three standard temperature scales (Celsius, Kelvin, and Fahrenheit).
The triple point of water is 273.16 K, and that is an international standard temperature point. The freezing point of water at one atmosphere pressure, 0.00°C, is 0.01K below that at 273.15 K. If you want to be really precise about it, the boiling point is 373.125 K, or 99.75 °C. But for general purposes, just 0 °C and 100 °C are precise enough.
While the typical treatment of temperature scales takes the freezing point of water to be 0C and the boiling point at standard pressure to be 100C, there are more precise treatments of standard points for defining temperatures. one standard point is the triple point of water which has been defined to be 273.16K. The freezing point of water at atmospheric pressure is .01K below this at 273.15K.
While the typical treatment of temperature scales takes the freezing point of water to be 0C and the boiling point at standard pressure to be 100C, there are more precise treatments of standard points for defining temperatures. one standard point is the triple point of water which has been defined to be 273.16K. The freezing point of water at atmospheric pressure is .01K below this at 273.15K.
That will be all now, the next lesson will be on the laws of thermodynamics
Was the economic impact of the Protestant-Catholic conflict more damaging to Northern Ireland than the political impact?
The Protestant-Catholic conflict often led to strikes and riots that disrupted production.
The constant violence in Northern Ireland drove away foreign investors who were worried about the security and profitability of their investments
Furthermore, tourists stayed away from Northern Ireland because they feared the terrorist attacks conducted by the IRA.
As a result, the economy became stagnant. A pull out of foreign companies led to massive unemployment. People who lost their jobs cut down on spending and this also led to the decline of local businesses. Without the tourist dollar, many companies suffered. Since the economic impact affected both Catholics and Protestants equally, it’s impact on Northern Ireland can be considered to be very damaging.
The conflict has had a more positive impact on Northern Ireland’s politics compared to its economy.
The Protestant-Catholic violence drew attention to the many unequal government policies and led to sweeping reforms.
For example, after 2 civil rights marches in 1968, the government decided to abolish the unfair voting system that only allowed property or business owners to vote, unfairly preventing many poorer Catholics from voting. The catastrophe of Bloody Sunday also led to a power sharing agreement between the Protestants and Catholics.
From this we can see that the political impact was largely positive and not damaging
Because of the tension and danger of conflict erupting, Protestants and Catholics lived separately
They went to different schools, churches and workplaces in order to minimize contact.
One example was the Belfast Peace Wall built in 1969. The aim of the wall was to separate Protestants and Catholics to keep them segregated and avoid conflict.
However, this had a mixed impact because while it did probably reduce the number of riots that occurred, it also kept the mutual suspicion between the Protestants and Catholics in place, since they had no opportunity to interact with each other. On the whole, the social impact of the conflict kept the rift between the two groups and therefore helped to continue its own existence.
Conclusion:
The political and economic impacts of the conflict were both very great since they affected the rights and livelihoods of both Protestants and Catholics. However, while they are equal in impact, the political impact of the conflict was mostly positive because it led to more equal rights, whereas the economic impact was negative because it resulted in massive unemployment. The social impact was not so great since the distrust between the Protestants and Catholics had already existed for hundreds of years. Therefore, it is true to say the economic and social impacts were more damaging than the political one.
The constant violence in Northern Ireland drove away foreign investors who were worried about the security and profitability of their investments
Furthermore, tourists stayed away from Northern Ireland because they feared the terrorist attacks conducted by the IRA.
As a result, the economy became stagnant. A pull out of foreign companies led to massive unemployment. People who lost their jobs cut down on spending and this also led to the decline of local businesses. Without the tourist dollar, many companies suffered. Since the economic impact affected both Catholics and Protestants equally, it’s impact on Northern Ireland can be considered to be very damaging.
The conflict has had a more positive impact on Northern Ireland’s politics compared to its economy.
The Protestant-Catholic violence drew attention to the many unequal government policies and led to sweeping reforms.
For example, after 2 civil rights marches in 1968, the government decided to abolish the unfair voting system that only allowed property or business owners to vote, unfairly preventing many poorer Catholics from voting. The catastrophe of Bloody Sunday also led to a power sharing agreement between the Protestants and Catholics.
From this we can see that the political impact was largely positive and not damaging
Because of the tension and danger of conflict erupting, Protestants and Catholics lived separately
They went to different schools, churches and workplaces in order to minimize contact.
One example was the Belfast Peace Wall built in 1969. The aim of the wall was to separate Protestants and Catholics to keep them segregated and avoid conflict.
However, this had a mixed impact because while it did probably reduce the number of riots that occurred, it also kept the mutual suspicion between the Protestants and Catholics in place, since they had no opportunity to interact with each other. On the whole, the social impact of the conflict kept the rift between the two groups and therefore helped to continue its own existence.
Conclusion:
The political and economic impacts of the conflict were both very great since they affected the rights and livelihoods of both Protestants and Catholics. However, while they are equal in impact, the political impact of the conflict was mostly positive because it led to more equal rights, whereas the economic impact was negative because it resulted in massive unemployment. The social impact was not so great since the distrust between the Protestants and Catholics had already existed for hundreds of years. Therefore, it is true to say the economic and social impacts were more damaging than the political one.
How far were the citizenship rights a cause of conflict between the Sinhalese and Tamils in Sri Lanka?
Since Sri Lanka became independent, there was an unequal criteria for citizenship rights in Sri Lanka. A citizen’s father and grandfather had to be born in Sri Lanka, meaning that many Indian Tamils were denied basic rights like voting although they had worked in the country for a long time. Although Sri Lanka negotiated with India to allow Indian Tamils to return to India, while giving the rest Sri Lankan citizenship in 1964, it did not hold up its end of the bargain, and 100,000 Tamils remain stateless.
This led to anger among the Tamils because they felt that their contributions to Sri Lanka had been ignored. Furthermore, they felt Sri Lanka had betrayed them by not fulfilling the 1964 agreement. Given that these policies were dictated by the Sinhalese, Tamil anger was inevitably directed at them, contributing to the Sri Lankan conflict.
However, there are other factors that contributed to the conflict. Before independence, unequal job opportunities already contributed to conflict. English-educated Tamils were given preference over the Sinhalese in the British civil service. This led the Sinhalese to resent the Tamils.
After independence, the situation was reversed when Sinhala was made the official language of government. Tamils who did not learn the language were dismissed. This caused the Tamils to blame the Sinhalese for their unfairness and the loss of jobs, leading to greater anger and worsening the conflict.
However, this factor is not as significant as citizenship rights in causing conflict. This is because the language policy was altered to accommodate Tamil majority areas.
For example, the 1978 Sri Lankan Constitution recognized Tamil as an official language and allowed it to be used to run the administration in the Tamil majority northern and eastern provinces.
Hence, since 1978, Tamils had less cause for resentment in this area, as they could work in the civil service. This lessens the potential for conflict because they did not lose out to the Sinhalese in Tamil majority provinces.
Equal opportunities were actually present before independence; university admissions were based on merit. However, the Sinhalese still resented the disproportionate number of Tamils entering university.
After independence, the Sinhalese government changed education policies that made it harder for Tamils and easier for the Sinhalese to enter university.
For example, Tamil students had to obtain higher admissions scores compared to the Sinhalese in order to get into the same course. Furthermore, quotas were set on the number of Tamils who could be admitted to any course. This led to a drop in the number of Tamils getting a tertiary education.
As a result, the Tamils felt that they were being victimized since they were deprived of higher education. They saw it as a deliberate attempt by the government to keep them in low-skilled, low-paying jobs. Hence, Tamil resentment was once again directed at the Sinhalese and worsened the conflict.
To a large extent, unequal citizenship rights contributed to the Sri Lankan conflict, since it enshrined unequal treatment of the Tamils under the law. However, this is not to the exclusion of unfair education policies that made the Tamils feel victimized by the Sinhalese. Unequal job opportunities, while also leading to the conflict, was not such a major factor since the unequal policy has been changed to allow Tamil to be an official language of administration. Therefore, Tamils had less cause for resentment in this area. This means that unequal citizenship rights and education policy contributed to the conflict to a larger extent.
This led to anger among the Tamils because they felt that their contributions to Sri Lanka had been ignored. Furthermore, they felt Sri Lanka had betrayed them by not fulfilling the 1964 agreement. Given that these policies were dictated by the Sinhalese, Tamil anger was inevitably directed at them, contributing to the Sri Lankan conflict.
However, there are other factors that contributed to the conflict. Before independence, unequal job opportunities already contributed to conflict. English-educated Tamils were given preference over the Sinhalese in the British civil service. This led the Sinhalese to resent the Tamils.
After independence, the situation was reversed when Sinhala was made the official language of government. Tamils who did not learn the language were dismissed. This caused the Tamils to blame the Sinhalese for their unfairness and the loss of jobs, leading to greater anger and worsening the conflict.
However, this factor is not as significant as citizenship rights in causing conflict. This is because the language policy was altered to accommodate Tamil majority areas.
For example, the 1978 Sri Lankan Constitution recognized Tamil as an official language and allowed it to be used to run the administration in the Tamil majority northern and eastern provinces.
Hence, since 1978, Tamils had less cause for resentment in this area, as they could work in the civil service. This lessens the potential for conflict because they did not lose out to the Sinhalese in Tamil majority provinces.
Equal opportunities were actually present before independence; university admissions were based on merit. However, the Sinhalese still resented the disproportionate number of Tamils entering university.
After independence, the Sinhalese government changed education policies that made it harder for Tamils and easier for the Sinhalese to enter university.
For example, Tamil students had to obtain higher admissions scores compared to the Sinhalese in order to get into the same course. Furthermore, quotas were set on the number of Tamils who could be admitted to any course. This led to a drop in the number of Tamils getting a tertiary education.
As a result, the Tamils felt that they were being victimized since they were deprived of higher education. They saw it as a deliberate attempt by the government to keep them in low-skilled, low-paying jobs. Hence, Tamil resentment was once again directed at the Sinhalese and worsened the conflict.
To a large extent, unequal citizenship rights contributed to the Sri Lankan conflict, since it enshrined unequal treatment of the Tamils under the law. However, this is not to the exclusion of unfair education policies that made the Tamils feel victimized by the Sinhalese. Unequal job opportunities, while also leading to the conflict, was not such a major factor since the unequal policy has been changed to allow Tamil to be an official language of administration. Therefore, Tamils had less cause for resentment in this area. This means that unequal citizenship rights and education policy contributed to the conflict to a larger extent.
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