Changes in state at constant pressure

From the Gibbs-Helmholtz equation we have, for a change in state at constant pressure and temperature,... 

In laboratory practice most changes in state are carried out under a constant atmospheric pressure, which is equal to the pressure of the system. The change in state at constant pressure can be envisioned by confining the system to a cylinder closed by a weighted... 

Figure 7.8 Change in state at constant pressure, (a) Initial state, (b) Final state.

Thus far we have observed that the Gibbs and Planck functions provide the criteria of spontaneity and equilibrium in isothermal changes of state at constant pressure. If we extend our analysis to systems in which other constraints are placed on the system, and therefore work other than mechanical work can be performed, we find that the Gibbs and Helmholtz functions also supply a means for calculating the maximum magnitude of work obtainable from an isothermal change. 

The Specific Latent Heat of a substance is the heat gained per unit mass without an accompanying rise in temperature during a change of state at constant pressure. It is measured in J/kg. 

The definition of G includes the enthalpy H, which is a particularly suitable energy function for description of changes of state at constant pressure p (see section 3.4). As seen from the following, the G function is also adapted to the description of equilibrium in systems of matter at constant pressure p. 

This relationship identifies the surface energy as the increment of the Gibbs free energy per unit change in area at constant temperature, pressure, and number of moles. The path-dependent variable dWs in Eq. (2.60) has been replaced by a state variable, namely, the Gibbs free energy. The energy interpretation of y has been carried to the point where it has been identified with a specific thermodynamic function. As a result, many of the relationships that apply to G also apply to y ... 

A system receives 93 J of electrical work, performs 227 J of pressure-volume work, and releases 155 J of heat. What is the change in internal energy of the system For each of the following chemical and physical changes carried out at constant pressure, state whether work is done by the system on the surroundings or by the surroundings on the system, or whether the amount of work is negligible. 

Further, for changes of state at constant composition, the forms of the Gibbs-Duhem equation in Table 6.3 can be related to derivatives in Table 6.2. For example, for a change in pressure at constant temperature and constant composition, (4.3.13) combines with (4.3.15) to yield... 

B) The volume = sum of the volume of the components is their standard states, i.e. AV or volume change for mixing is zero. When the volume change is nil at constant pressure, the change in enthalpy (heat content) is also zero. 

For the four piston apparatus the change in M, (4.7), is the same as the change in G, since all reservoirs are at constant pressure and temperature. Similarly we may consider the change in M at the pressure of the stationary state, for which we have... 

If a change from state A to state B occurs in a system at constant pressure (isobaric) so that only p V work is done, then w = pA V and... 

The standard molar enthalpy of formation of a compound, AH , is equal to the enthalpy change when one mole of the compound is formed at a constant pressure of 1 atm and a fixed temperature, ordinarily 25°C, from the elements in their stable states at that pressure and temperature. From the equations... 

We have seen that a constant-pressure calorimeter and a constant-volume bomb calorimeter measure changes in different state functions at constant volume, the heat transfer is interpreted as A U at constant pressure, it is interpreted as AH. However, it is sometimes necessary to convert the measured value of AU into AH. For example, it is easy to measure the heat released by the combustion of glucose in a bomb calorimeter, but to use that information in assessing energy changes in metabolism, which take place at constant pressure, we need the enthalpy of reaction. 

For a finite process in which the system changes from state 1 to state 2, the work done at constant pressure is... 

The change in Gibbs s free energy (defined, as stated, for a system at constant pressure and temperature) when a moles of A and b moles of B are converted into c moles of C and d moles of D is AG = cpc +dpD - apA - bpB, where p represent chemical potentials , i.e. free energy per mole of the substances, defined in terms of concentration of a component X as... 

The energy relations associated with the redox processes in wastewater follow the general rules of thermodynamics (Castellan, 1975 Atkins, 1978). The Gibbs free energy, G, of the system is the major thermodynamic function defining the state — and the change in state — of the biochemical redox processes. At constant temperature and under constant pressure, AG is equal to the maximum work, which can be produced by the redox process ... 

Hess s law, or the law of constant heat summation, states that at constant pressure, the enthalpy change for a process is not dependent on the reaction pathway, but is dependent only upon the initial and final states of the system. The enthalpy changes of individual steps in a reaction can be added or subtracted to obtain the net enthalpy change for the overall reaction. 

Much more information can be obtained from the DSC experiment than simply an observation of the transition from a solid to a liquid phase. A plot of heat flow against temperature is a true depiction of the continuity of the heat capacity at constant pressure (Cp). If the entire temperature range of a given process is known, the physical state of a material will reflect the usefulness of that material at any temperature point on the plot. For polyethylene terephthalate (see Fig. 4.9), a stepshaped transition is interpreted as a change in Cp resulting from a... 

Let us first consider how the density of the condensed phase changes with temperature. As our material in the vapour phase is cooled at constant pressure the density increases until the boiling point is reached. Further cooling then allows us to differentiate between the vapour and liquid states by the formation of a boundary. Further cooling increases the liquid density but at a much slower rate than that of the gaseous phase. The density of many liquids can be described by a simple linear equation over a wide temperature range 5... 

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