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104-406: 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

208-416: A closed system (i.e. there is no transfer of matter into or out of the system), the first law states that the change in internal energy of the system ( Δ U system ) is equal to the difference between the heat supplied to the system ( Q ) and the work ( W ) done by the system on its surroundings. (Note, an alternate sign convention , not used in this article, is to define W as the work done on

312-427: A rubber balloon . Some reaction may occur in a battery even if no external current is flowing. There is usually a coupling coefficient , which may depend on relative rates, which determines what percentage of the driving free energy is turned into external work, or captured as "chemical work", a misnomer for the free energy of another chemical process. Laws of thermodynamics The laws of thermodynamics are

416-412: A thermodynamic system is the energy of the system as a state function , measured as the quantity of energy necessary to bring the system from its standard internal state to its present internal state of interest, accounting for the gains and losses of energy due to changes in its internal state, including such quantities as magnetization . It excludes the kinetic energy of motion of the system as

520-405: A closed system changed is in its doing of work on its surroundings. Such work may be simply mechanical, as when the system expands to drive a piston, or, for example, when the system changes its electric polarization so as to drive a change in the electric field in the surroundings. If the system is not closed, the third mechanism that can increase the internal energy is transfer of substance into

624-446: A constant value as its temperature approaches absolute zero . At absolute zero temperature, the system is in the state with the minimum thermal energy, the ground state . The constant value (not necessarily zero) of entropy at this point is called the residual entropy of the system. With the exception of non-crystalline solids (e.g. glass ) the residual entropy of a system is typically close to zero. However, it reaches zero only when

728-418: A cylinder closed with a piston, it can proceed only by doing work on the piston. The extent variable for the reaction can increase only if the piston moves out, and conversely if the piston is pushed inward, the reaction is driven backwards. Similarly, a redox reaction might occur in an electrochemical cell with the passage of current through a wire connecting the electrodes . The half-cell reactions at

832-495: A finite rate, producing entropy. This can be made even more explicit by introducing the reaction rates d ξ j /d t . For every physically independent process (Prigogine & Defay, p. 38; Prigogine, p. 24) This is a remarkable result since the chemical potentials are intensive system variables, depending only on the local molecular milieu. They cannot "know" whether temperature and pressure (or any other system variables) are going to be held constant over time. It

936-457: A function only of extensive state variables is the one and only cardinal function of state for the generation of Massieu functions. It is not itself customarily designated a 'Massieu function', though rationally it might be thought of as such, corresponding to the term 'thermodynamic potential', which includes the internal energy. For real and practical systems, explicit expressions of the fundamental equations are almost always unavailable, but

1040-450: A mutual thermodynamic equilibrium. The sum of the entropies of the initially isolated systems is less than or equal to the total entropy of the final combination. Equality occurs just when the two original systems have all their respective intensive variables (temperature, pressure) equal; then the final system also has the same values. The second law is applicable to a wide variety of processes, both reversible and irreversible. According to

1144-530: A positive affinity for each other. The differential of G takes on a simple form that displays its dependence on composition change If there are a number of chemical reactions going on simultaneously, as is usually the case, with a set of reaction coordinates { ξ j  }, avoiding the notion that the amounts of the components (  N i  ) can be changed independently. The expressions above are equal to zero at thermodynamic equilibrium , while they are negative when chemical reactions proceed at

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1248-501: A series of three papers, the most famous one being the paper On the Equilibrium of Heterogeneous Substances . In these papers, Gibbs showed how the first two laws of thermodynamics could be measured graphically and mathematically to determine both the thermodynamic equilibrium of chemical reactions as well as their tendencies to occur or proceed. Gibbs’ collection of papers provided the first unified body of thermodynamic theorems from

1352-407: A set of scientific laws which define a group of physical quantities , such as temperature , energy , and entropy , that characterize thermodynamic systems in thermodynamic equilibrium . The laws also use various parameters for thermodynamic processes , such as thermodynamic work and heat , and establish relationships between them. They state empirical facts that form a basis of precluding

1456-471: A set of extensive parameters X i (energy, mass, entropy, number of particles and so on) and thermodynamic forces F i (related to their related intrinsic parameters, such as temperature and pressure), the Onsager theorem states that where i , k = 1,2,3,... index every parameter and its related force, and are called the thermodynamic flows. Internal energy The internal energy of

1560-410: A system (as work , heat , or matter ), the system's internal energy changes in accordance with the law of conservation of energy . The second law of thermodynamics states that in a natural thermodynamic process , the sum of the entropies of the interacting thermodynamic systems never decreases. A common corollary of the statement is that heat does not spontaneously pass from a colder body to

1664-463: A system arises as the sum of the motions of all the system's particles with respect to the center-of-mass frame, whether it be the motion of atoms, molecules, atomic nuclei, electrons, or other particles. The microscopic potential energy algebraic summative components are those of the chemical and nuclear particle bonds, and the physical force fields within the system, such as due to internal induced electric or magnetic dipole moment , as well as

1768-428: A system in the energy representation . As a function of state , its arguments are exclusively extensive variables of state. Alongside the internal energy, the other cardinal function of state of a thermodynamic system is its entropy, as a function, S ( U , V ,{ N j }) , of the same list of extensive variables of state, except that the entropy, S , is replaced in the list by the internal energy, U . It expresses

1872-437: A system that is in thermodynamic contact equilibrium with a heat reservoir, each microstate has an energy E i {\displaystyle E_{i}} and is associated with a probability p i {\displaystyle p_{i}} . The internal energy is the mean value of the system's total energy, i.e., the sum of all microstate energies, each weighted by its probability of occurrence: This

1976-453: A system undergoes certain phase transformations while being heated, such as melting and vaporization, it may be observed that the temperature of the system does not change until the entire sample has completed the transformation. The energy introduced into the system while the temperature does not change is called latent energy or latent heat , in contrast to sensible heat, which is associated with temperature change. Thermodynamics often uses

2080-412: A useful and convenient theoretical limiting case, all natural processes are irreversible. A prime example of this irreversibility is the transfer of heat by conduction or radiation. It was known long before the discovery of the notion of entropy that when two bodies, initially of different temperatures, come into direct thermal connection, then heat immediately and spontaneously flows from the hotter body to

2184-564: A variety of interesting and important ways. One of the simplest is the Clausius statement, that heat does not spontaneously pass from a colder to a hotter body. It implies the existence of a quantity called the entropy of a thermodynamic system. In terms of this quantity it implies that When two initially isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium with itself but not necessarily with each other, are then allowed to interact, they will eventually reach

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2288-408: A warmer body. The third law of thermodynamics states that a system's entropy approaches a constant value as the temperature approaches absolute zero . With the exception of non-crystalline solids ( glasses ), the entropy of a system at absolute zero is typically close to zero. The first and second laws prohibit two kinds of perpetual motion machines, respectively: the perpetual motion machine of

2392-466: A way that one can advance only if the other also does. The coupling may occasionally be rigid , but it is often flexible and variable. In solution chemistry and biochemistry , the Gibbs free energy decrease (∂ G /∂ ξ , in molar units, denoted cryptically by Δ G ) is commonly used as a surrogate for (− T times) the global entropy produced by spontaneous chemical reactions in situations where no work

2496-403: A whole and the potential energy of position of the system as a whole, with respect to its surroundings and external force fields. It includes the thermal energy, i.e. , the constituent particles' kinetic energies of motion relative to the motion of the system as a whole. The internal energy of an isolated system cannot change, as expressed in the law of conservation of energy , a foundation of

2600-417: A wide variety of fields. The non-equilibrium thermodynamics has been applied for explaining how ordered structures e.g. the biological systems, can develop from disorder. Even if Onsager's relations are utilized, the classical principles of equilibrium in thermodynamics still show that linear systems close to equilibrium always develop into states of disorder which are stable to perturbations and cannot explain

2704-423: A zeroth law was later added to allow for a self-consistent definition of temperature. Additional laws have been suggested, but have not achieved the generality of the four accepted laws, and are generally not discussed in standard textbooks. The zeroth law of thermodynamics provides for the foundation of temperature as an empirical parameter in thermodynamic systems and establishes the transitive relation between

2808-425: Is This is useful if the equation of state is known. In case of an ideal gas, we can derive that d U = C V d T {\displaystyle dU=C_{V}\,dT} , i.e. the internal energy of an ideal gas can be written as a function that depends only on the temperature. The expression relating changes in internal energy to changes in temperature and volume is The equation of state

2912-412: Is extensive in these variables), and that it is weakly convex . Knowing temperature and pressure to be the derivatives T = ∂ U ∂ S , {\displaystyle T={\frac {\partial U}{\partial S}},} P = − ∂ U ∂ V , {\displaystyle P=-{\frac {\partial U}{\partial V}},}

3016-419: Is a purely local criterion and must hold regardless of any such constraints. Of course, it could have been obtained by taking partial derivatives of any of the other fundamental state functions, but nonetheless is a general criterion for (− T times) the entropy production from that spontaneous process; or at least any part of it that is not captured as external work. (See Constraints below.) We now relax

3120-410: Is an extensive property : it depends on the size of the system, or on the amount of substance it contains. At any temperature greater than absolute zero , microscopic potential energy and kinetic energy are constantly converted into one another, but the sum remains constant in an isolated system (cf. table). In the classical picture of thermodynamics, kinetic energy vanishes at zero temperature and

3224-403: Is an intensive measure, this energy expresses the concept as an extensive property of the system, often referred to as the thermal energy , The scaling property between temperature and thermal energy is the entropy change of the system. Statistical mechanics considers any system to be statistically distributed across an ensemble of N {\displaystyle N} microstates . In

Chemical thermodynamics - Misplaced Pages Continue

3328-471: Is being done; or at least no "useful" work; i.e., other than perhaps ±  P d V . The assertion that all spontaneous reactions have a negative ΔG is merely a restatement of the second law of thermodynamics , giving it the physical dimensions of energy and somewhat obscuring its significance in terms of entropy. When no useful work is being done, it would be less misleading to use the Legendre transforms of

3432-426: Is measured under conditions of constant volume (at STP condition), as in a closed rigid container such as a bomb calorimeter . However, at constant pressure, as in reactions in vessels open to the atmosphere, the measured heat is usually not equal to the internal energy change, because pressure-volume work also releases or absorbs energy. (The heat change at constant pressure is called the enthalpy change; in this case

3536-430: Is not dependent on other thermodynamic quantities such as pressure or density. The internal energy of an ideal gas is proportional to its amount of substance (number of moles) N {\displaystyle N} and to its temperature T {\displaystyle T} where c V {\displaystyle c_{V}} is the isochoric (at constant volume) molar heat capacity of

3640-458: Is not possible to construct a machine which will perpetually output work without an equal amount of energy input to that machine. Or more briefly, a perpetual motion machine of the first kind is impossible. The second law of thermodynamics indicates the irreversibility of natural processes, and in many cases, the tendency of natural processes to lead towards spatial homogeneity of matter and energy, especially of temperature. It can be formulated in

3744-427: Is now known as the third law, was formulated by Walther Nernst over the period 1906–1912. While the numbering of the laws is universal today, various textbooks throughout the 20th century have numbered the laws differently. In some fields, the second law was considered to deal with the efficiency of heat engines only, whereas what was called the third law dealt with entropy increases. Gradually, this resolved itself and

3848-400: Is the joule (J). The internal energy relative to the mass with unit J/kg is the specific internal energy . The corresponding quantity relative to the amount of substance with unit J/ mol is the molar internal energy . The internal energy of a system depends on its entropy S, its volume V and its number of massive particles: U ( S , V ,{ N j }) . It expresses the thermodynamics of

3952-402: Is the energy that can be released when chemical substances undergo a transformation through a chemical reaction . Breaking and making chemical bonds involves energy release or uptake, often as heat that may be either absorbed by or evolved from the chemical system. Energy released (or absorbed) because of a reaction between chemical substances ("reactants") is equal to the difference between

4056-410: Is the ideal gas law Solve for pressure: Substitute in to internal energy expression: Take the derivative of pressure with respect to temperature: Replace: And simplify: To express d U {\displaystyle \mathrm {d} U} in terms of d T {\displaystyle \mathrm {d} T} and d V {\displaystyle \mathrm {d} V} ,

4160-451: Is the statistical expression of the law of conservation of energy . Thermodynamics is chiefly concerned with the changes in internal energy Δ U {\displaystyle \Delta U} . For a closed system, with mass transfer excluded, the changes in internal energy are due to heat transfer Q {\displaystyle Q} and due to thermodynamic work W {\displaystyle W} done by

4264-571: The electrodes are constrained if no current is allowed to flow. The current might be dissipated as Joule heating , or it might in turn run an electrical device like a motor doing mechanical work . An automobile lead - acid battery can be recharged, driving the chemical reaction backwards. In this case as well, the reaction is not an independent process. Some, perhaps most, of the Gibbs free energy of reaction may be delivered as external work. The hydrolysis of ATP to ADP and phosphate can drive

Chemical thermodynamics - Misplaced Pages Continue

4368-674: The entropy representation . Each cardinal function is a monotonic function of each of its natural or canonical variables. Each provides its characteristic or fundamental equation, for example U = U ( S , V ,{ N j }) , that by itself contains all thermodynamic information about the system. The fundamental equations for the two cardinal functions can in principle be interconverted by solving, for example, U = U ( S , V ,{ N j }) for S , to get S = S ( U , V ,{ N j }) . In contrast, Legendre transformations are necessary to derive fundamental equations for other thermodynamic potentials and Massieu functions . The entropy as

4472-421: The first law of thermodynamics . The notion has been introduced to describe the systems characterized by temperature variations, temperature being added to the set of state parameters, the position variables known in mechanics (and their conjugated generalized force parameters), in a similar way to potential energy of the conservative fields of force, gravitational and electrostatic. Internal energy changes equal

4576-406: The force -times- distance work delivered by living muscles , and synthesis of ATP is in turn driven by a redox chain in mitochondria and chloroplasts , which involves the transport of ions across the membranes of these cellular organelles . The coupling of processes here, and in the previous examples, is often not complete. Gas can leak slowly past a piston, just as it can slowly leak out of

4680-435: The ideal gas law P V = N R T {\displaystyle PV=NRT} immediately follows as below: The above summation of all components of change in internal energy assumes that a positive energy denotes heat added to the system or the negative of work done by the system on its surroundings. This relationship may be expressed in infinitesimal terms using the differentials of each term, though only

4784-407: The surroundings , or it may simply be dissipated , appearing as T times a corresponding increase in the entropy of the system and its surrounding. Or it may go partly toward doing external work and partly toward creating entropy. The important point is that the extent of reaction for a chemical reaction may be coupled to the displacement of some external mechanical or electrical quantity in such

4888-485: The 'difference of information entropy between them'. This defines how much additional microscopic physical information is needed to specify one of the macroscopically specified states, given the macroscopic specification of the other – often a conveniently chosen reference state which may be presupposed to exist rather than explicitly stated. A final condition of a natural process always contains microscopically specifiable effects which are not fully and exactly predictable from

4992-498: The algebraic sum of the heat transferred and the work done. In systems without temperature changes, potential energy changes equal the work done by/on the system. The internal energy cannot be measured absolutely. Thermodynamics concerns changes in the internal energy, not its absolute value. The processes that change the internal energy are transfers, into or out of the system, of substance, or of energy, as heat , or by thermodynamic work . These processes are measured by changes in

5096-463: The amounts of the components (  N i  ) can be changed independently. All real processes obey conservation of mass , and in addition, conservation of the numbers of atoms of each kind. Consequently, we introduce an explicit variable to represent the degree of advancement of a process, a progress variable   ξ for the extent of reaction (Prigogine & Defay, p. 18; Prigogine, pp. 4–7; Guggenheim, p. 37.62), and to

5200-508: The application of thermodynamics to chemistry . The primary objective of chemical thermodynamics is the establishment of a criterion for 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: The following state functions are of primary concern in chemical thermodynamics: Most identities in chemical thermodynamics arise from application of

5304-466: The body as a whole. In statistical mechanics , the internal energy of a body can be analyzed microscopically in terms of the kinetic energies of microscopic motion of the system's particles from translations , rotations , and vibrations , and of the potential energies associated with microscopic forces, including chemical bonds . The unit of energy in the International System of Units (SI)

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5408-431: The colder one. Entropy may also be viewed as a physical measure concerning the microscopic details of the motion and configuration of a system, when only the macroscopic states are known. Such details are often referred to as disorder on a microscopic or molecular scale, and less often as dispersal of energy . For two given macroscopically specified states of a system, there is a mathematically defined quantity called

5512-488: The composition (the amounts of each chemical substance , expressed as the numbers of molecules present or the numbers of moles ). Explicitly, For the case where only PV work is possible, a restatement of the fundamental thermodynamic relation , in which μ i is the chemical potential for the i -th component in the system The expression for d G is especially useful at constant T and P , conditions, which are easy to achieve experimentally and which approximate

5616-411: The concept of the ideal gas for teaching purposes, and as an approximation for working systems. The ideal gas consists of particles considered as point objects that interact only by elastic collisions and fill a volume such that their mean free path between collisions is much larger than their diameter. Such systems approximate monatomic gases such as helium and other noble gases . For an ideal gas

5720-430: The conditions in living creatures While this formulation is mathematically defensible, it is not particularly transparent since one does not simply add or remove molecules from a system. There is always a process involved in changing the composition; e.g., a chemical reaction (or many), or movement of molecules from one phase (liquid) to another (gas or solid). We should find a notation which does not seem to imply that

5824-423: The contribution of such a field to the energy due to the coupling of the internal degrees of freedom of the object with the field. In such a case, the field is included in the thermodynamic description of the object in the form of an additional external parameter. For practical considerations in thermodynamics or engineering, it is rarely necessary, convenient, nor even possible, to consider all energies belonging to

5928-496: The definition of temperature in a non-circular way without reference to entropy, its conjugate variable . Such a temperature definition is said to be 'empirical'. The first law of thermodynamics is a version of the law of conservation of energy , adapted for thermodynamic processes. In general, the conservation law states that the total energy of an isolated system is constant; energy can be transformed from one form to another, but can be neither created nor destroyed. In

6032-438: The distinction between independent processes and coupling . Contrary to the clear implications of many reference sources, the previous analysis is not restricted to homogeneous , isotropic bulk systems which can deliver only P d V work to the outside world, but applies even to the most structured systems. There are complex systems with many chemical "reactions" going on at the same time, some of which are really only parts of

6136-400: The energy content of the products and the reactants. This change in energy is called the change in internal energy of a chemical system. It can be calculated from Δ f U r e a c t a n t s o {\displaystyle \Delta _{\rm {f}}U_{\mathrm {reactants} }^{\rm {o}}} , the internal energy of formation of

6240-488: The energy of deformation of solids ( stress - strain ). Usually, the split into microscopic kinetic and potential energies is outside the scope of macroscopic thermodynamics. Internal energy does not include the energy due to motion or location of a system as a whole. That is to say, it excludes any kinetic or potential energy the body may have because of its motion or location in external gravitational , electrostatic , or electromagnetic fields . It does, however, include

6344-619: The entropy appropriate for constant T , or for constant T and P , the Massieu functions − F/T and − G/T , respectively. Generally the systems treated with the conventional chemical thermodynamics are either at equilibrium or near equilibrium. Ilya Prigogine developed the thermodynamic treatment of open systems that are far from equilibrium. In doing so he has discovered phenomena and structures of completely new and completely unexpected types. His generalized, nonlinear and irreversible thermodynamics has found surprising applications in

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6448-414: The first and second laws of thermodynamics, particularly the law of conservation of energy , to these state functions. The three laws of thermodynamics (global, unspecific forms): 1. The energy of the universe is constant. 2. In any spontaneous process, there is always an increase in entropy of the universe. 3. The entropy of a perfect crystal (well ordered) at 0 Kelvin is zero. Chemical energy

6552-437: The first kind which produces work with no energy input, and the perpetual motion machine of the second kind which spontaneously converts thermal energy into mechanical work. The history of thermodynamics is fundamentally interwoven with the history of physics and the history of chemistry , and ultimately dates back to theories of heat in antiquity. The laws of thermodynamics are the result of progress made in this field over

6656-413: The fourth law of thermodynamics. They describe the relation between thermodynamic flows and forces in non-equilibrium thermodynamics , under the assumption that thermodynamic variables can be defined locally in a condition of local equilibrium . These relations are derived from statistical mechanics under the principle of microscopic reversibility (in the absence of external magnetic fields ). Given

6760-470: The free-energy functions depend on the composition , as do all the extensive thermodynamic potentials , including the internal energy. If the quantities {  N i  }, the number of chemical species , are omitted from the formulae, it is impossible to describe compositional changes. For an unstructured, homogeneous "bulk" system, there are still various extensive compositional variables {  N i  } that G depends on, which specify

6864-417: The functional relations exist in principle. Formal, in principle, manipulations of them are valuable for the understanding of thermodynamics. The internal energy U {\displaystyle U} of a given state of the system is determined relative to that of a standard state of the system, by adding up the macroscopic transfers of energy that accompany a change of state from the reference state to

6968-399: The gas; c V {\displaystyle c_{V}} is constant for an ideal gas. The internal energy of any gas (ideal or not) may be written as a function of the three extensive properties S {\displaystyle S} , V {\displaystyle V} , N {\displaystyle N} (entropy, volume, number of moles ). In case of

7072-413: The given state of the system from the reference state. From a non-relativistic microscopic point of view, it may be divided into microscopic potential energy, U micro,pot {\displaystyle U_{\text{micro,pot}}} , and microscopic kinetic energy, U micro,kin {\displaystyle U_{\text{micro,kin}}} , components: The microscopic kinetic energy of

7176-407: The given state: where Δ U {\displaystyle \Delta U} denotes the difference between the internal energy of the given state and that of the reference state, and the E i {\displaystyle E_{i}} are the various energies transferred to the system in the steps from the reference state to the given state. It is the energy needed to create

7280-400: The ideal gas it is in the following way where c o n s t {\displaystyle \mathrm {const} } is an arbitrary positive constant and where R {\displaystyle R} is the universal gas constant . It is easily seen that U {\displaystyle U} is a linearly homogeneous function of the three variables (that is, it

7384-458: The important physical fact that temperature is one-dimensional and that one can conceptually arrange bodies in a real number sequence from colder to hotter. These concepts of temperature and of thermal equilibrium are fundamental to thermodynamics and were clearly stated in the nineteenth century. The name 'zeroth law' was invented by Ralph H. Fowler in the 1930s, long after the first, second, and third laws were widely recognized. The law allows

7488-414: The internal energy gives rise to the temperature of the system. Statistical mechanics relates the pseudo-random kinetic energy of individual particles to the mean kinetic energy of the entire ensemble of particles comprising a system. Furthermore, it relates the mean microscopic kinetic energy to the macroscopically observed empirical property that is expressed as temperature of the system. While temperature

7592-428: The internal energy is an exact differential . For a closed system, with transfers only as heat and work, the change in the internal energy is expressing the first law of thermodynamics . It may be expressed in terms of other thermodynamic parameters. Each term is composed of an intensive variable (a generalized force) and its conjugate infinitesimal extensive variable (a generalized displacement). For example,

7696-443: The internal energy is purely potential energy. However, quantum mechanics has demonstrated that even at zero temperature particles maintain a residual energy of motion, the zero point energy . A system at absolute zero is merely in its quantum-mechanical ground state, the lowest energy state available. At absolute zero a system of given composition has attained its minimum attainable entropy . The microscopic kinetic energy portion of

7800-399: The internal energy. It is distributed between microscopic kinetic and microscopic potential energies. In general, thermodynamics does not trace this distribution. In an ideal gas all of the extra energy results in a temperature increase, as it is stored solely as microscopic kinetic energy; such heating is said to be sensible . A second kind of mechanism of change in the internal energy of

7904-470: The kinetic energy consists only of the translational energy of the individual atoms. Monatomic particles do not possess rotational or vibrational degrees of freedom, and are not electronically excited to higher energies except at very high temperatures . Therefore, the internal energy of an ideal gas depends solely on its temperature (and the number of gas particles): U = U ( N , T ) {\displaystyle U=U(N,T)} . It

8008-444: The macroscopic specification of the initial condition of the process. This is why entropy increases in natural processes – the increase tells how much extra microscopic information is needed to distinguish the initial macroscopically specified state from the final macroscopically specified state. Equivalently, in a thermodynamic process, energy spreads. The third law of thermodynamics can be stated as: A system's entropy approaches

8112-523: The mathematical framework of chemical thermodynamics. In 1865, the German physicist Rudolf Clausius , in his Mechanical Theory of Heat , suggested that the principles of thermochemistry , e.g. the heat evolved in combustion reactions , could be applied to the principles of thermodynamics . Building on the work of Clausius, between the years 1873-76 the American mathematical physicist Willard Gibbs published

8216-433: The mechanical work done by the system may be related to the pressure P {\displaystyle P} and volume change d V {\displaystyle \mathrm {d} V} . The pressure is the intensive generalized force, while the volume change is the extensive generalized displacement: This defines the direction of work, W {\displaystyle W} , to be energy transfer from

8320-524: The nineteenth and early twentieth centuries. The first established thermodynamic principle, which eventually became the second law of thermodynamics, was formulated by Sadi Carnot in 1824 in his book Reflections on the Motive Power of Fire . By 1860, as formalized in the works of scientists such as Rudolf Clausius and William Thomson , what are now known as the first and second laws were established. Later, Nernst's theorem (or Nernst's postulate), which

8424-584: The number of possible microstates according to the Boltzmann principle where S is the entropy of the system, k B is the Boltzmann constant , and Ω the number of microstates. At absolute zero there is only 1 microstate possible ( Ω = 1 as all the atoms are identical for a pure substance, and as a result all orders are identical as there is only one combination) and ln ⁡ ( 1 ) = 0 {\displaystyle \ln(1)=0} . The Onsager reciprocal relations have been considered

8528-410: The occurrence of ordered structures. Prigogine called these systems dissipative systems , because they are formed and maintained by the dissipative processes which take place because of the exchange of energy between the system and its environment and because they disappear if that exchange ceases. They may be said to live in symbiosis with their environment. The method which Prigogine used to study

8632-406: The partial derivative where we introduce a concise and historical name for this quantity, the " affinity ", symbolized by A , as introduced by Théophile de Donder in 1923.(De Donder; Progogine & Defay, p. 69; Guggenheim, pp. 37, 240) The minus sign ensures that in a spontaneous change, when the change in the Gibbs free energy of the process is negative, the chemical species have

8736-417: The possibility of certain phenomena, such as perpetual motion . In addition to their use in thermodynamics , they are important fundamental laws of physics in general and are applicable in other natural sciences . Traditionally, thermodynamics has recognized three fundamental laws, simply named by an ordinal identification, the first law, the second law, and the third law. A more fundamental statement

8840-482: The principles developed by others, such as Clausius and Sadi Carnot . During the early 20th century, two major publications successfully applied the principles developed by Gibbs to chemical processes and thus established the foundation of the science of chemical thermodynamics. The first was the 1923 textbook Thermodynamics and the Free Energy of Chemical Substances by Gilbert N. Lewis and Merle Randall . This book

8944-409: The reactant molecules related to the bond energies of the molecules under consideration, and Δ f U p r o d u c t s o {\displaystyle \Delta _{\rm {f}}U_{\mathrm {products} }^{\rm {o}}} , the internal energy of formation of the product molecules. The change in internal energy is equal to the heat change if it

9048-440: The requirement of a homogeneous "bulk" system by letting the chemical potentials and the affinity apply to any locality in which a chemical reaction (or any other process) is occurring. By accounting for the entropy production due to irreversible processes, the equality for d G is now replaced by or Any decrease in the Gibbs function of a system is the upper limit for any isothermal , isobaric work that can be captured in

9152-407: The same, overall process. An independent process is one that could proceed even if all others were unaccountably stopped in their tracks. Understanding this is perhaps a " thought experiment " in chemical kinetics , but actual examples exist. A gas-phase reaction at constant temperature and pressure which results in an increase in the number of molecules will lead to an increase in volume. Inside

9256-500: The second law, in a reversible heat transfer, an element of heat transferred, δ Q {\displaystyle \delta Q} , is the product of the temperature ( T {\displaystyle T} ), both of the system and of the sources or destination of the heat, with the increment ( d S {\displaystyle dS} ) of the system's conjugate variable, its entropy ( S {\displaystyle S} ): While reversible processes are

9360-423: The stability of the dissipative structures to perturbations is of very great general interest. It makes it possible to study the most varied problems, such as city traffic problems, the stability of insect communities, the development of ordered biological structures and the growth of cancer cells to mention but a few examples. In this regard, it is crucial to understand the role of walls and other constraints , and

9464-404: The sum of the internal energies of the two initial systems, U 1 and U 2 : U s y s t e m = U 1 + U 2 . {\displaystyle U_{\rm {system}}=U_{1}+U_{2}.} The First Law encompasses several principles: Combining these principles leads to one traditional statement of the first law of thermodynamics: it

9568-430: The system by its surroundings): Δ U s y s t e m = Q − W . {\displaystyle \Delta U_{\rm {system}}=Q-W.} For processes that include the transfer of matter, a further statement is needed. When two initially isolated systems are combined into a new system, then the total internal energy of the new system, U system , will be equal to

9672-399: The system has a unique ground state (i.e., the state with the minimum thermal energy has only one configuration, or microstate ). Microstates are used here to describe the probability of a system being in a specific state, as each microstate is assumed to have the same probability of occurring, so macroscopic states with fewer microstates are less probable. In general, entropy is related to

9776-448: The system on its surroundings. Accordingly, the internal energy change Δ U {\displaystyle \Delta U} for a process may be written Δ U = Q − W (closed system, no transfer of substance) . {\displaystyle \Delta U=Q-W\quad {\text{(closed system, no transfer of substance)}}.} When a closed system receives energy as heat, this energy increases

9880-443: The system's properties, such as temperature, entropy , volume, electric polarization, and molar constitution . The internal energy depends only on the internal state of the system and not on the particular choice from many possible processes by which energy may pass into or out of the system. It is a state variable , a thermodynamic potential , and an extensive property . Thermodynamics defines internal energy macroscopically, for

9984-752: The system. This increase, Δ U m a t t e r {\displaystyle \Delta U_{\mathrm {matter} }} cannot be split into heat and work components. If the system is so set up physically that heat transfer and work that it does are by pathways separate from and independent of matter transfer, then the transfers of energy add to change the internal energy: Δ U = Q − W + Δ U matter (matter transfer pathway separate from heat and work transfer pathways) . {\displaystyle \Delta U=Q-W+\Delta U_{\text{matter}}\quad {\text{(matter transfer pathway separate from heat and work transfer pathways)}}.} If

10088-432: The temperatures of multiple bodies in thermal equilibrium. The law may be stated in the following form: If two systems are both in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. Though this version of the law is one of the most commonly stated versions, it is only one of a diversity of statements that are labeled as "the zeroth law". Some statements go further, so as to supply

10192-637: The term used for the chemical potential energy is chemical potential , and sometimes the Gibbs-Duhem equation is used. In most cases of interest in chemical thermodynamics there are internal degrees of freedom and processes, such as chemical reactions and phase transitions , which create entropy in the universe unless they are at equilibrium or are maintained at a "running equilibrium" through "quasi-static" changes by being coupled to constraining devices, such as pistons or electrodes , to deliver and receive external work. Even for homogeneous "bulk" systems,

10296-428: The total intrinsic energy of a sample system, such as the energy given by the equivalence of mass. Typically, descriptions only include components relevant to the system under study. Indeed, in most systems under consideration, especially through thermodynamics, it is impossible to calculate the total internal energy. Therefore, a convenient null reference point may be chosen for the internal energy. The internal energy

10400-507: The use of the partial derivative ∂ G /∂ ξ (in place of the widely used "Δ G ", since the quantity at issue is not a finite change). The result is an understandable expression for the dependence of d G on chemical reactions (or other processes). If there is just one reaction If we introduce the stoichiometric coefficient for the i-th component in the reaction (negative for reactants), which tells how many molecules of i are produced or consumed, we obtain an algebraic expression for

10504-432: The widely tabulated enthalpies of formation are used.) A related term is the heat of combustion , which is the chemical energy released due to a combustion reaction and of interest in the study of fuels . Food is similar to hydrocarbon and carbohydrate fuels, and when it is oxidized, its energy release is similar (though assessed differently than for a hydrocarbon fuel — see food energy ). In chemical thermodynamics,

10608-516: The working system to the surroundings, indicated by a positive term. Taking the direction of heat transfer Q {\displaystyle Q} to be into the working fluid and assuming a reversible process , the heat is where T {\displaystyle T} denotes the temperature , and S {\displaystyle S} denotes the entropy . The change in internal energy becomes The expression relating changes in internal energy to changes in temperature and volume

10712-410: Was later labelled as the zeroth law after the first three laws had been established. The zeroth law of thermodynamics defines thermal equilibrium and forms a basis for the definition of temperature: If two systems are each in thermal equilibrium with a third system, then they are in thermal equilibrium with each other. The first law of thermodynamics states that, when energy passes into or out of

10816-466: Was responsible for supplanting the chemical affinity with the term free energy in the English-speaking world. The second was the 1933 book Modern Thermodynamics by the methods of Willard Gibbs written by E. A. Guggenheim . In this manner, Lewis, Randall, and Guggenheim are considered as the founders of modern chemical thermodynamics because of the major contribution of these two books in unifying

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