Temperature thermodynamic definition

To calculate the entropy of a substance, we use Boltzmann s formula, but the calculations are sometimes very difficult and require a lot of manipulation of Eq. 6. To measure the entropy of a substance, we use the thermodynamic definition, Eq. 1, in combination with the third law of thermodynamics. Because the third law tells us that S(0) = 0 and Eq. 2 can be used to calculate the change in entropy as a substance is heated to the temperature of interest, we can write... 

The requirements for the thermodynamic definition of solubility are 1) well defined initial solid and final solution states, and 2) establishment of equilibrium between these two states. Under these conditions, the solubility at a given temperature and pressure is the concentration of the sample in solution. At a given temperature and pressure, the solid state is the stable crystalline state and the solution state is... 

The thermodynamic definition of entropy says that the change in entropy dS in a process carried out reversibly is the heat absorbed in the process d Qrev divided by the temperature... 

The thermodynamic temperature. Hie definition of thermodynamic temperature in kelvins (Eq. 6-8) also follows from Eq. 6-6. See textbooks of thermodynamics for further treatment. 

Entropy is a measure of the degree of randomness in a system. The change in entropy occurring with a phase transition is defined as the change in the system s enthalpy divided by its temperature. This thermodynamic definition, however, does not correlate entropy with molecular structure. For an interpretation of entropy at the molecular level, a statistical definition is useful. Boltzmann (1896) defined entropy in terms of the number of mechanical states that the atoms (or molecules) in a system can achieve. He combined the thermodynamic expression for a change in entropy with the expression for the distribution of energies in a system (i.e., the Boltzman distribution function). The result for one mole is ... 

Set out the relevant form of the thermodynamic definition of K value. At this low system pressure, the vapor-phase nonideahty is negligible. Since neither component has a very high vapor pressure at the system temperature, and since the differences between the vapor pressures and the system pressure are relatively small, the pure-liquid fugacities can be taken to be essentially the same as the vapor pressures. 

Like pressure and volume, temperature is a thing of everyday experience and most people think they understand it, at least to the extent of being able to say that it is a measure of how hot or cold a body is relative to our senses. Giving a precise definition is more difficult, however. Also, the scales most commonly used to measure this quantity, Celsius and (less frequently these days) Fahrenheit, are arbitrary. The thermodynamic definition, ensconced in the zeroth law, essentially states that if there is no heat flow between two bodies, they are at the same temperature. This is not very enlightening and we will have to wait until we discuss what the molecules are doing to get more insight. Nevertheless, the idea that tempera-... 

This is a crude model, but hopefully you now see how the calculus of probabilities, as Maxwell put it, explains why heat flows downhill (from hot to cold), why a gas expands to occupy its container and why the world is. . . getting more disordered and generally going to hell in a hand-basket We also hope that you now have a feel for entropy that cannot be obtained from the purely thermodynamic definition of heat divided by temperature, hi principle, calculating the entropy of a system would now seem to be easy. Just count the num-... 

The thermodynamic definition of the spinodal, binodal and critical point were given earlier by Eqs. (9), (7) and (8) respectively. The variation of AG with temperature and composition and the resulting phase diagram for a UCST behaviour were illustrated in Fig. 1. It is well known that the classical Flory-Huggins theory is incapable of predicting an LCST phase boundary. If has, however, been used by several authors to deal with ternary phase diagrams Other workers have extensively used a modified version of the classical model to explain binary UCST or ternary phase boundaries The more advanced equation-of-state theories, such as the theory... 

When we add an electron to the system at a given temperature and pressure, the electron is necessarily positioned in a level close to The increase in free energy of the electron system due to the addition of one electron is hence (Figure 5). Hence, the Fermi-Dirac occupation function is in accordance with the thermodynamic definition of the electrochemical potential. 

If the volume, temperature and the number of moles are taken as constant, then the explicit thermodynamic definition of surface tension may be written from Equations (203) and... 

Figure 23.1 is a psychrometric chart for the air-water system. It shows the relationship between the temperature (abscissa) and absolute humidity (ordinale, in g water per kg dry air) of humid air from 0°C to 130°C at one atmosphere absolute pressure. Line as representing percent humidity and adiabatic saturation are drawn according to the thermodynamic definitions of these terms. Equations for the adiabatic saturation and wet-bulb temperature lines on the chart are as follows (Geankoplis 1983) ... 

It is possible to use the standard thermodynamic equations to convert the thermally corrected internal energy into the enthalpies and Gibbs free energies at the same temperature. To determine the enthalpy, the thermodynamic definition of enthalpy is used. 

Initial concepts of temperature came from the physical sensation of the relative hotness or coldness of bodies. This sensation of warmth or cold is so subjective relative to our immediate prior exposure that it is difficult to use for anything but simple qualitative comparison. The need to assign a quantitative value to temperature leads to the definition of a temperature scale. The concept of fixed points of temperature arises from the observation that there exist some systems in nature that always exhibit the same temperatures. The scientific or thermodynamic definition of temperature comes from Kelvin, who defined the ratio of the thermodynamic or absolute temperatures of two systems as being equal to the ratio of the heat added to the heat rejected for a reversible heat engine operated between the systems. This unique temperature scale requires only one fixed point, the triple point of water, for its definition. 

The temperature and pressure dependences of the distribution constant can be easily derived from the temperature and pressure dependences of the right hand sides of equations 45 and 48. According to the well-known thermodynamic definitions it may be written for LLC systems... 

Note that from Eq 2.4 the thermodynamic definitions of a pressure, P, and temperature T, are ... 

In a ferromagnetic system the order parameter is given by the spontaneous magnetization, M, which in an ideal second-order transition rises from zero at 7J-(see, e.g., Belov 1959). As mentioned in sect. 2, and are related by C, — TdM IQ T and therefore, if the temperature of the maximum of is taken as the thermodynamical definition of T., it corresponds to the maximum slope of M. Many authors define TJ- (T for us) as the temperature where the maximum slope of extrapolates to Ms = 0. Although this is not a thermodynamical definition, the difference ATc = 7 — Tc is a measure of the fluctuations above Tq as was mentioned in sect. 2. 

Standard potential values are usually those of ideal unimolal solutions at a pressure of 1 atm (ignoring the deviations of fugacity and activity from pressure and concentration, respectively). A pressure of 1 bar = 10 Pa was recommended as the standard value to be used in place of 1 atm = 101 325 Pa (the difference corresponds to a 0.34-mV shift of potential). If a component of the gas phase participates in the equilibrium, its partial pressure is taken as the standard value if not, the standard pressure should be that of the inert gas over the solution or melt. In a certain case, a standard potential can be established in a system with nonunity activities, if the combination of the latter substituted in the Nemst equation equals unity. For any sohd component of redox systems, the chemical potential does not change in the course of the reaction, and it remains in its standard state. In contrast to the common thermodynamic definition of the standard state, the temperature is ignored, because the potential of the standard hydrogen (protium) electrode is taken to be zero at any temperature in aqueous and protic media. The zero temperature coefficient of the SHE corresponds to the conventional assumption of... 

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