Absolute temperature entropy

Gibbs free energy) = (enthalpy) - (absolute temperature)(entropy)... 

There are an infinite number of other integrating factors X with corresponding fiinctions ( ) the new quantities T and. S are chosen for convenience.. S is, of course, the entropy and T, a fiinction of 0 only, is the absolute temperature , which will turn out to be the ideal-gas temperature, 0jg. The constant C is just a scale factor detennining the size of the degree. 

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)...

The polymerization of THE is an equilibrium polymerization. It fits the equation that relates the enthalpy of polymerization, AH, and entropy of polymerization at 1 Af, to the equilibrium monomer concentration, [Af as a function of the absolute temperature, T, where R is the gas constant... 

A heat engine is a device operating in cycles that takes in heat, from a heat reservoir at temperature Tp, discards heat, to another heat reservoir at a lower temperature T, and produces work. A heat reservoir is a body that can absorb or reject unlimited amounts of heat without change in temperature. Entropy changes of a heat reservoir depend only on the absolute temperature and on the quantity of heat transferred, and are always given by the integrated form of equation 4 ... 

Cp = specific heat e = specific internal energy h = enthalpy k =therm conductivity p = pressure, s = specific entropy t = temperature T = absolute temperature u = specific internal energy [L = viscosity V = specific volume f = subscript denoting saturated hquid g = subscript denoting saturated vapor... 

S is the entropy, T the absolute temperature, p the pressure, and V the volume. These are also state functions, in that the entropy is specified once two variables (like T andp) are specified, for example. Likewise,... 

The work done by an expanding fluid is defined as the difference in internal energy between the fluid s initial and final states. Most thermodynamic tables and graphs do not presentbut only h, p, v, T (the absolute temperature), and s (the specific entropy). Therefore, u must be calculated with the following equation ... 

The second law of thermodynamics also consists of two parts. The first part is used to define a new thermodynamic variable called entropy, denoted by S. Entropy is the measure of a system s energy that is unavailable for work.The first part of the second law says that if a reversible process i f takes place in a system, then the entropy change of the system can be found by adding up the heat added to the system divided by the absolute temperature of the system when each small amount of heat is added ... 

For any reversible process, the increase in entropy of any participating system is equal to the heat absorbed by that system divided by the absolute temperature at which the transfer occurred. That is, for a system, i. 

The equation (16) shows that the increase of bound energy in a reversible isothermal change is equal to the increase of entropy multiplied by the absolute temperature, so that the entropy may be regarded as the capacity for bound energy in such changes. B will evidently contain the arbitrary term / IT. 

The increase of energy per unit increase of entropy at constant volume is measured by the absolute temperature. 

The entropy of a condensed chemically homogeneous substance vanishes at the zero of absolute temperature ... 

In summary, the Carnot cycle can be used to define the thermodynamic temperature (see Section 2.2b), show that this thermodynamic temperature is an integrating denominator that converts the inexact differential bq into an exact differential of the entropy dS, and show that this thermodynamic temperature is the same as the absolute temperature obtained from the ideal gas. This hypothetical engine is indeed a useful one to consider. 

The entropies of all perfect crystals approach zero as the absolute temperature approaches zero. 

The most common states of a pure substance are solid, liquid, or gas (vapor), state property See state function. state symbol A symbol (abbreviation) denoting the state of a species. Examples s (solid) I (liquid) g (gas) aq (aqueous solution), statistical entropy The entropy calculated from statistical thermodynamics S = k In W. statistical thermodynamics The interpretation of the laws of thermodynamics in terms of the behavior of large numbers of atoms and molecules, steady-state approximation The assumption that the net rate of formation of reaction intermediates is 0. Stefan-Boltzmann law The total intensity of radiation emitted by a heated black body is proportional to the fourth power of the absolute temperature, stereoisomers Isomers in which atoms have the same partners arranged differently in space, stereoregular polymer A polymer in which each unit or pair of repeating units has the same relative orientation, steric factor (P) An empirical factor that takes into account the steric requirement of a reaction, steric requirement A constraint on an elementary reaction in which the successful collision of two molecules depends on their relative orientation. 

Although reactions in which molecules are cleaved into two or more pieces have favorable entropy effects, many potential cleavages do not take place because of large increases in enthalpy. An example is cleavage of ethane into two methyl radicals. In this case, a bond of 79 kcal mol (330 kJ mol ) is broken, and no new bond is formed to compensate for this enthalpy increase. However, ethane can be cleaved at very high temperatures, which illustrates the principle that entropy becomes more important as the temperature increases, as is obvious from the equation AG = AH — TAS. The enthalpy term is independent of temperature, while the entropy term is directly proportional to the absolute temperature. 

There is no single criterion for the system alone that applies to all processes. However, if we restrict the conditions to constant temperature and pressure, there is a state function whose change for the system predicts spontaneity. This new state function is the free energy (G), which was introduced by the American J. Willard Gibbs and is defined by Equation G = H - T S As usual, H is enthalpy, T is absolute temperature, and S is entropy. 

For the purpose of illustrating the application of the thermodynamic equation of state to experimental data, consider the plot given in Fig. 84 for the retractive force, measured at fixed length, against the absolute temperature for a hypothetical elastic substance. The slope at any temperature T gives the important quantity —(dS/dL)T,p according to Eq. (12) an increase in / with T at constant L shows immediately, therefore, that the entropy decreases with increase in length... 

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