Isobaric temperature change, reversible

If an isobaric temperature change is carried out reversibly, the heat exchanged in the process can be substituted into the expression for the entropy change, and the equations at constant pressure when no work is performed other than PV work are... 

Since, for reversible cycles, in an isobaric temperature-volume change of pure substances, d / I .v = TdS + VdP, then by rearrangement, one obtains... 

These class II derivatives are extensive measurable state functions. Both and Cp are always positive, so U (H) always increases with isometric (isobaric) increases in T. The heat capacities are experimentally accessible by measuring the temperature change that accompanies addition of a small amount of energy (such as heat) to a system at constant volume, to yield C , or reversibly at constant pressure, to yield Cp that is. 

Using the data in Table 3.1 and the heat capacity expression = CpdT, find the entropy change for a sample of 1.0 mol of oxygen that undergoes an isobaric reversible temperature change from 300 to 400 K. 

Thus, in a reversible process that is both isothermal and isobaric, dG equals the work other than pressure-volume work that occurs in the process." Equation (3.96) is important in chemistry, since chemical processes such as chemical reactions or phase changes, occur at constant temperature and constant pressure. Equation (3.96) enables one to calculate work, other than pressure-volume work, for these processes. Conversely, it provides a method for incorporating the variables used to calculate these forms of work into the thermodynamic equations. 

Besides the reversible and irreversible processes, there are other processes. Changes implemented at constant pressure are called isobaric process, while those occurring at constant temperature are known as isothermal processes. When a process is carried out under such conditions that heat can neither leave the system nor enter it, one has what is called an adiabatic process. A vacuum flask provides an excellent example a practical adiabatic wall. When a system, after going through a number of changes, reverts to its initial state, it is said to have passed through a cyclic process. 

Recall from Section 12.1 that a true reversible process is an idealization it is a process in which the system proceeds with infinitesimal speed through a series of equilibrium states. The external pressure therefore, can never differ by more than an infinitesimal amount from the pressure, P, of the gas itself. The heat, work, energy, and enthalpy changes for ideal gases at constant volume (called isochoric processes) and at constant pressure (isobaric processes) have already been considered. This section examines isothermal (constant temperature) and adiabatic (q = 0) processes. 

A storage device that couples a high-temperature hydride to a phase change material has been tested by Arthur D. Little Inc. This system uses the heat released during hydrogenation to melt the material. In the reverse process, the released solidification energy is taken to liberate the hydrogen from the hydride compound. The material used is a Mg powder coated with Ni by means of chemical vapor deposition. The system was successfully tested as an essentially isothermal and isobaric process [29]. 

Assume a system containing 5.00 mol of ideal gas at the pressure 101325 Pa. In its initial state (1), the gas temperature is 100 °C. By an isobaric and reversible cooling, the gas temperature is reduced to 0 °C in the final state (2). The molar heat capacity of the gas Cp = 20.8 J/molK is assumed to be constant. Calculate the change in the internal energy AU of the system during the process ... 

---