The third law of thermodynamics

From the third law of thermodynamics, the entiopy 5 = 0 at 0 K makes it possible to calculate S at any temperature from statistical thermodynamics within the hamionic oscillator approximation (Maczek, 1998). From this, A5 of formation can be found, leading to A/G and the equilibrium constant of any reaction at 298 K for which the algebraic sum of AyG for all of the constituents is known. A detailed knowledge of A5, which we already have, leads to /Gq at any temperature. Variation in pressure on a reacting system can also be handled by classical thermodynamic methods. 

This is an expression of Nernst s postulate which may be stated as the entropy change in a reaction at absolute zero is zero. The above relationships were established on the basis of measurements on reactions involving completely ordered crystalline substances only. Extending Nernst s result, Planck stated that the entropy, S0, of any perfectly ordered crystalline substance at absolute zero should be zero. This is the statement of the third law of thermodynamics. The third law, therefore, provides a means of calculating the absolute value of the entropy of a substance at any temperature. The statement of the third law is confined to pure crystalline solids simply because it has been observed that entropies of solutions and supercooled liquids do not approach a value of zero on being cooled. 

The second and third laws of thermodynamics The second law and the definition of entropy... 

Statistical mechanics affords an accurate method to evaluate ArSP, provided that the necessary structural and spectroscopic parameters (moments of inertia, vibrational frequencies, electronic levels, and degeneracies) are known [1], As this computation implicitly assumes that the entropy of a perfect crystal is zero at the absolute zero, and this is one of the statements of the third law of thermodynamics, the procedure is called the third law method. 

A disordered state of a system (state of high entropy) can be achieved in more ways (W) than an ordered state and is therefore more probable. The entropy of a state can be calculated from Boltzmann s formula, S = k In W. According to the third law of thermodynamics, the entropy of a pure, perfectly ordered crystalline substance at 0 K is zero. 

Third law of thermodynamics The entropy of a pure substance in a perfect crystalline state is zero at absolute zero. 

Also, since at T = 0 K, S for most solids is zero (Third Law of Thermodynamics), the graph of G versus T will start off (at T = 0) having a zero gradient (i.e. being parallel to the T axis) (see Figure 18.1). 

If water or some other compound with a simple molecular structure has been studied, it is possible to combine the entropy of vaporization, A5 = AHyl T, with the third-law calorimetric entropy of the liquid to obtain a thermodynamic value for the entropy of the vapor. The statistical mechanical value of Sg can be calculated using the known molar mass and the spectroscopic parameters for the rotation and vibration of the gas-phase molecule. A comparison of Sg (thermodynamic) with Sg (spectroscopic) provides a test of the validity of the third law of thermodynamics. The case of H2O is particularly interesting, since ice has a nonzero residual entropy at 0 K due to frozen-in disorder in the proton positions. ... 

This function may be calculated from molecular data by tlie methods of quantum statistical mechanics. It may also be obtained from experimentally determined heat capacity data, from which the required entropies are deduced using the third law of thermodynamics. The calculation may be put into several equivalent forms, and is discussed in the text-books. An account of the theory is given by Fowler and Guggenheim 7 its application by... 

According to the third law of thermodynamics, the entropy of a perfect crystal should be zero at 0° K at all pressures hence, it follows that... 

Third Law of Thermodynamics The entropy of a hypothetical pure, perfect, crystalline substance at absolute zero temperature is zero. 

According to the third law of thermodynamics, the residual entropy S(0) (the temperature-independent, "frozen-in" disorder) of a perfect crystal is zero at absolute zero temperature. S(0)>0 for amorphous materials and for crystals with defects and/or imperfections. It cannot be calculated for such materials by using the equations developed in this book. It has been shown... 

Finally it is appropriate to consider the third law of thermodynamics briefly in connection with the detennination of entropy values. So far we have related entropy to molecular disorder—the greater the disorder or freedom of motion of the atoms or molecules in a system, the greater the entropy of the system. The most ordered arrangement of any substance with the least freedom of atomic or molecular motion is a perfect crystalline substance at absolute zero (0 K). It follows, therefore, that the lowest entropy any substance can attain is that of a perfect crystal at absolute zero. According to the third law of thermodynamics, the entropy of a perfect crystalline substance is zero at the absolute zero of temperature. As the temperature increases, the freedom of motion also increases. Thus the entropy of any substance at a temperature above 0 K is greater than zero. Note also that if the crystal is impure or if it has defects, then its entropy is greater than zero even at 0 K because it would not be perfectly ordered. 

Third law of thermodynamics. The entropy of a perfect crystalline substance is zero at the absolute zero of temperature. (18.2)... 

Show how, using the Third Law of Thermodynamics, the free energy change of a chemical reaction may be calculated from calorimetric data. 

Let s state the third law of thermodynamics. The law states that pure and perfect crystalline substances have an entropy of zero at 0 Kelvin. What does that mean It means that a pure crystalline substance will have perfect order at absolute zero temperature. An increase in temperature will destroy this zero entropy. By looking at the graph (Figure 10-1), it is clear that an increase in temperature increases the entropy. 

Figure 4.2. As we approach absolute zero, the slope of the curve approaches zero as required by the third law of thermodynamics. (The entropy of any pure substance in complete internal equilibrium is zero.) An empirical relationship that fits the data for several ceramics is...

According to the third law of thermodynamics, the entropy of a perfect crystalline substance is zero at the absolute zero of temperature. As the temperature increases, the freedom of motion increases and hence also the number of microstates. Thus, the entropy of any substance at a temperature above 0 K is greater than zero. Note also... 

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