{"id":943,"date":"2019-10-14T14:24:53","date_gmt":"2019-10-14T14:24:53","guid":{"rendered":"http:\/\/chemdictionary.org\/?p=943"},"modified":"2019-10-14T15:08:04","modified_gmt":"2019-10-14T15:08:04","slug":"entropy-equation","status":"publish","type":"post","link":"https:\/\/chemdictionary.org\/entropy-equation\/","title":{"rendered":"Entropy Equation"},"content":{"rendered":"\n

Introduction<\/strong><\/h2>\n\n\n\n

An Entropy contains a broad\nrange of properties of a thermodynamic system. It relates to the number \u03a9 of microscopic configuration which is\nalso known as microstates which are consistent with the macroscopic quantitates\nthat characterize the system i.e. volume, pressure, and temperature.<\/p>\n\n\n\n

History<\/strong><\/h2>\n\n\n\n

Lazare\nCarnot, a French mathematician suggested in his 1803 paper named Fundamental\nPrinciples of Equilibrium and Movement in any machine represents moment losses\nby activities through acceleration and shocks of the moving parts. From the\nbasis of this work, in 1824 Lazare’s son Sadi Carnot published Reflections on\nthe Motive Power OF Fire which suggested that in every heat-engines, whenever\nheat (caloric) decreases through a temperature difference i.e. from a hot to a\ncold body, motive power or work can be produced. He made an analogy of a water\nwheel that how water is fallen on it. This gives an initial idea to the second\nlaw of thermodynamics. In the early 18th<\/sup> century, Carnot tells us\nthat both heat and light were indestructible forms of matter that are attracted\nand repelled by other matter and he took this view from the Newtonian\nHypothesis.<\/p>\n\n\n\n

In 1843, James Joule gives the\nfirst law of thermodynamics, from his experiments on heat-friction expresses\nthe concept of energy and its conservation in all processes. However, it\ndoesn\u2019t tell us the effects of friction and dissipation.<\/p>\n\n\n\n

During the 1850s and 1860s, a\nGerman physicist named Rudolf Clausius objects to the supposition that no\nchange occurs in a working body and gave this change a mathematical explanation\nby interrogating the nature of the inherent loss of usable heat when work is\ndone. For example, the heat produced by friction. Clausius explained entropy as\nthe transformation content in contrast to an earlier view that was based on the\ntheories of Newton that heat was an indestructible particle having a mass. <\/p>\n\n\n\n

Later an entropy was given a\nstatistical basis by different scientists named Ludwig Boltzmann, Josiah\nWillard Gibbs and James Clerk Maxwell. In 1877 Boltzmann tells us the way to\nmeasure the entropy of ideal gas particles in which he explained the entropy\nthat it is directly proportional to the natural logarithm of the number of\nmicrostates that gas can occupy. Hence, the crucial problem in statistical\nthermodynamics has been to illustrate the distribution of a given amount of\nenergy E over N identical system<\/p>\n\n\n\n

Definition<\/strong><\/h2>\n\n\n\n

A measure of an extent to\nwhich energy is dispersed is called entropy.<\/p>\n\n\n\n

Entropy can be defined as the\ntwo equivalent definitions:<\/p>\n\n\n\n

  1. The classical thermodynamic definition<\/li>
  2. The statistical mechanics’ definition<\/li><\/ol>\n\n\n\n

    The ancient definition of\nclassical thermodynamics was first developed. In the classical thermodynamics point,\nthe microscopic features of a system are not considered. While the behavior of\na system is illustrated in terms of empirically defined thermodynamic variables\nsuch as entropy, temperature, heat capacity, and pressure. The classical\nthermodynamics explanation describes a state of equilibrium whereas more\nattempts have been made to develop an appropriate definition of entropy in a non-equilibrium\nsystem. Hence, the macroscopic approach in studying thermodynamics that does\nnot require any knowledge about the behavior of individual particles is known\nas classical thermodynamics.<\/p>\n\n\n\n

    The statistical definition of\nentropy and other properties of thermodynamic were developed later. The\nthermodynamic properties are defined in terms of the statistics of the motions\nof the microscopic constituents of a system. in short, the statistical\nthermodynamics is defined as an elaborated approach which is based on the\naverage behavior of large groups of individual particles.<\/p>\n\n\n\n

    Entropy Equations<\/p>\n\n\n\n

    Entropy can be calculated\nusing different equations:<\/p>\n\n\n\n

    1. If the process is at a constant temperature, then the equation will be:<\/li><\/ol>\n\n\n\n
      \"\"<\/figure><\/div>\n\n\n\n

      Where <\/p>\n\n\n\n

      \u0394S indicated the change in entropy<\/p>\n\n\n\n

      qrev<\/sub> shows the reverse of the heat<\/p>\n\n\n\n

      T is the Kelvin temperature<\/p>\n\n\n\n

      • If there is a known reaction, then \u0394Srxn can be determined by using a table of standard entropy values.<\/li><\/ul>\n\n\n\n
        \"\"<\/figure><\/div>\n\n\n\n
        • Gibbs free energy (\u0394G) and the enthalpy (\u0394H) can also be used to determine \u0394S. The Gibbs entropy formula is :<\/li><\/ul>\n\n\n\n
          \"\"<\/figure><\/div>\n\n\n\n

          The entropy of a system<\/strong><\/p>\n\n\n\n

          entropy is a fundamental\nfunction of a state. It arises directly from the Carnot cycle. It can also be\nexplained as a reversible heat divided by temperature.<\/p>\n\n\n\n

          In a thermodynamic system, the\nphysical states like pressure, density, and temperature tend to be uniform over\ntime because the equilibrium state has a higher probability than any other\nstate.<\/p>\n\n\n\n

          For example, if an icy water\nglass is placed in the air at room temperature. The difference in temperature\nbetween ice water and a warm room starts to equalize itself as portions of the\nthermal energy from warm surroundings to cool icy water. A time comes when the\ntemperature of the room and a glass content becomes equal. Therefore, you can\nsay that the entropy of the room has decreased when the energy is dispersed to\nglass content.<\/p>\n\n\n\n

          The above example tells that it is an isolated system, the entropy of the glass content system has increased more than the entropy of the surrounding room has decreased. So it is seen that in an isolated system the diffusion of energy from warm to cool results in a net increase in entropy. Hence, when the “universe” of the room and glass content system reached an equilibrium temperature, the entropy change from an initial state is at maximum. So, the entropy of the thermodynamic system is a measure of how far the equalization has progressed. <\/p>\n\n\n\n

          Entropy never decreases for an\nisolated system. The increase in an entropy leads to an irreversible change in\na system because some of the energy is expended as waste heat that limits the\namount of work a system can perform. Entropy can only be calculated; it can\nnever be observed directly. For a given substance, entropy can be calculated as\na standard molar entropy from an absolute zero which is also known as absolute\nentropy or as a difference in entropy from any reference state which can also\nbe known as zero entropy. <\/p>\n\n\n\n

          Units\nof entropy:<\/strong><\/h2>\n\n\n\n

          Entropy has the dimension of\nenergy that is divided by temperature. So it has the units of Joules per Kelvin\n(J\/K) in SI units. These units are the same as that of heat capacity but off\ncourse both of the concepts are distinct. <\/p>\n\n\n\n

          Note<\/em><\/strong><\/p>\n\n\n\n

          Entropy is not a conserved\nquantity; for example, consider an isolated system having a non-uniform\ntemperature, the heat might flow irreversibly hence the temperature becomes\nuniform such that entropy increases. The second law of thermodynamics tells us\nthat entropy of a closed system remains constant or may increase. The chemical\nreactions are a source of changes in entropy and entropy also plays an\nimportant role in explaining the direction of a chemical reaction that proceeds\nspontaneously.<\/p>\n\n\n\n

          The definition of entropy\naccording to one dictionary is that “it is a measure of thermal energy per\nunit temperature that is not available for any useful work”. At a uniform\ntemperature, a substance has a maximum entropy and is unable to drive a heat\nengine. At non-uniform temperature, a substance has low entropy and some of the\nthermal energy can drive a heat engine.<\/p>\n\n\n\n

          There is a special case of entropy occurs when two or more different substances are mixed and hence the entropy of mixing takes place with an increase in entropy. If the substances are at the same temperature and pressure, the net exchange of heat and work will be zero. The entropy change is different due to the mixing of different substances. This results due to a change in volume per particle with mixing at a statistical mechanical level.<\/p>\n\n\n\n

          \"\"<\/figure><\/div>\n\n\n\n

          Experimental\nmeasurement of entropy:<\/strong><\/p>\n\n\n\n

          The entropy of a substance can be measured indirectly. The definition of temperature will be used in terms of entropy whereas limiting the energy exchange to heat (dU to dQ ).<\/p>\n\n\n\n

          \"\"<\/figure>\n\n\n\n

          The above relation shows how\nentropy changes dS when at a specific temperature a small amount of energy dQ\nis introduced into a system.<\/p>\n\n\n\n

          The measurement process goes\nas follows. At first, a given sample is cooled close to absolute zero. The\nentropy approaches zero at such temperatures because of the temperature\ndefinition. Then a small amount of heat is introduced into the sample and\ntemperature change is measured until the desired temperature is achieved i.e.\n25\u1d52C. The data gained is put into the above equation and the results yield the\nabsolute value of entropy of the sample at the final temperature. This value of\nentropy is called as calorimetric entropy<\/em>.<\/p>\n\n\n\n

          The\nsecond law of thermodynamics:<\/strong><\/p>\n\n\n\n

          the second law of\nthermodynamics generally requires that the total entropy of a system can\u2019t\ndecrease until increasing the entropy of any other system. So the entropy of an\nisolated system tends not to decrease. It follows that without the application\nof some work the transfer of heat from the cold body to a hot body is not\npossible. It is also impossible for any device that operates on a cycle to\nproduce total work from one reservoir of temperature; the total work production\nneeds a flow of heat from a hot reservoir to a cold reservoir or a single\nexpanding reservoir that undergoes adiabatic cooling that performs adiabatic\nwork. As a result, there is no possibility of a permanent motion system.<\/p>\n\n\n\n

          Applications:<\/strong><\/p>\n\n\n\n

          1. The fundamental thermodynamic relation:<\/strong><\/li><\/ol>\n\n\n\n

            The\nentropy of any system depends on its internal energy and its external\nparameters i.e. volume. In the thermodynamic limit, this fact leads us to an\nequation that relates the change in the internal energy U to changes in entropy\nand the external parameters. We call this relation a fundamental thermodynamic\nrelation. If the external pressure p holds on volume V as the only external\nparameter, then we gain the following relation: <\/p>\n\n\n\n

            dU = T\ndS \u2013 p dV<\/em><\/strong><\/p>\n\n\n\n

            This\nfundamental thermodynamic relation is involving many thermodynamic identities\nthat are independent of the microscopic details of the system. For example,\nMaxwell relations and heat capacities relationships.  <\/p>\n\n\n\n