Heat capacity free energy change

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

It appears that there are two temperatures of a universal nature that describe the thermodynamic properties for the dissolution of liquid hydrocarbons into water. The first of these, 7h is the temperature at which the heat of solution is zero and has a value of approximately 20°C for a variety of liquids. The second universal temperature is Ts, where the standard-state entropy change is zero and, as noted, Ts is about 140°C. The standard-state free energy change can be expressed in terms of these two temperatures, requiring knowledge only of the heat capacity change for an individual substance... 

As stated earlier, the most important applications of chemical and metallurgical thermodynamics are in the processes of synthesis, extraction, refining, etc. The free energy change is by far the most important of the thermodynamic properties as it is linked to identifying the limits of an actual process. The free energy in turn is dependent on other parameters like activity, interaction co-efficient, entropy, enthalpy, heat capacity, etc. 

Pfeil (1981) concluded that a-lactalbumin is less stable than lysozyme, with a lower thermal transition temperature, lower denaturational enthalpy, lower heat capacity change, and lower Gibbs free-energy change. 

ProTherm (16) is a large collection of thermodynamic data on protein stability, which has information on 1) protein sequence and stmcture (2) mutation details (wild-type and mutant amino acid hydrophobic to polar, charged to hydrophobic, aliphatic to aromatic, etc.), 3) thermodynamic data obtained from thermal and chemical denaturation experiments (free energy change, transition temperature, enthalpy change, heat capacity change, etc.), 4) experimental methods and conditions (pH, temperature, buffer and ions, measurement and method, etc.), 5) functionality (enzyme activity, binding constants, etc.), and 6) literature. 

Table 1 lists the thermodynamic functions of some inhibitors studied previously. The free energy change, AG°, is directly determined from the logarithm of the inhibition constant (i.e. RTlnKj), the enthalpy, entropy and heat capacity are the fitting results by using eq 7 where K, is replaced by Kj. Based on Scheme I, by using the relative thermodynamic functions (AAG°, AAH°, T°AAS°) given by... 

From temperature dependence data and other environmental factors, it is possible to evaluate the standard free energy change, AF , the molal changes in heat content (A// ), entropy (AS ) and heat capacity at constant pressure (ACp) which occur when the dissociation reaction occurs under standard conditions. 

We have now introduced the necessary basics for determining the association constant (ATa), standard free energy change (AG°), standard enthalpy change (AH°), standard entropy change (AS°), and standard heat capacity change (ACp for the complexation of a host and a guest. In subsequent sections, we detail practical aspects of these measurements. 

The free energy change at 673 K from this equation is AG(673 K) = 5.19 kcal/mol H2. The heat capacity and entropy of ThH2 are estimated from that of CeH2, Ce [5], and Th. With these and other calorimetric data of the elements [6] and the Th compounds, the enthalpy change of reaction (12) is calculated as AH298 = 25.8 kcal/mol H2 [4]. 

Fig. 2.4 A schematic showing the change in (a) the first and (b) the second derivatives of the free energy at the glass transition. The dash-dotted lines in (a) highlight that occurs over a range of temperatures dependent on the quench rate. It is important to note that while the specific heat capacity in (b) changes sharply, it is not discontinuous (Adapted from Greaves and Sen [25], Reprinted with permission from Taylor and Francis Ltd. http //www.informaworld.com)...

You can predict the free energy change AF of a system if you know AU and AS from heat capacity measurements. You can also use heat capacities to predict the equilibrium temperatures of objects in thermal contact. Let s revisit Example 7.2, in which two objects are brought into thermal contact. 

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