Isothermal change of state

The second step is the evaluation of the change in fugacity of the liquid with a change in pressure to a value above or below For this isothermal change of state from saturated liquid at to liquid at pressure P, Eq. (4-105) is integrated to give... 

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. 

Any physical interpretation of the Helmholtz energy must be based on interpreting Equation (4.3). Thus, for an isothermal change of state, the equation becomes... 

When SP [T] = SP"[0] (condition 2), AS°[T] can be expressed as v (SP [T] — Sp"[0]) that is, in terms of the observed quantities. We use the difference (Sp [T] — SP"[0]) as the absolute value of the entropy, which is equivalent to assigning the value of zero to SP"[0]. The two effects for which this assignment is valid are (1) the nuclear effects including those of nuclear spin, provided that the isothermal change of state does not involve a nuclear reaction and (2) the isotopic effects, provided there is no change in the isotopic composition of the substances. 

Steam at 13,000 kPa and 380°C undergoes an isothermal change of state to a pressure of 275 Determine the ratio of the fugacity in the final state to that in the initial state. 

Every isothermal change of state, of great intensity, is accom-panied by a liberation of heat. 

If, however, the isothermal change of state considered is purely a function of the volume, such that increase or decrease of the volume causes the change to proceed reversibly in one direction or the other, the problem is very simple for the work done against the external pressure is the value of A required. 

A similar equation can. be obtained by differentiating Boyle s law,pv = constant, for an isothermal change of state. The result is that... 

Closed systems. For reversible isothermal changes of state in closed systems, we have dN = = dJVp,- = 0, and F — Fgj-f. Then, combining (3.7.6) for the reversible heat... 

For the calculation of ETFE foil cushions under wind loads, thermodynamic laws have to be considered. The investigation of the load-bearing behaviour under wind loads supposes that the molar mass of the air enclosed inside the cushion and the temperature during the exposure are approximately constant. Therefore, the third gas law of Boyle-Mariotte with isothermal change of state according to equation 6.3 is used to analyse the structural behaviour. The third gas law of Boyle-Mariotte is ... 

The equilibrium condition for an isobaric and isothermal change of state for an open system is... 

For an elastic material the work done can be equated to a change in the stored elastic energy U. In the case of rubbers, it is usual to consider a reversible isothermal change of state at constant volume, so that the work done can be equated to the change in the Helmholtz free energy A, i.e. A17 = A 4. Here U is... 

The viscoelastic functions as defined refer to isothermal changes of state, and indeed the control of constant temperature is an important feature of all the experimental methods described in this chapter. It is evident, however, that the dynamic measurements described in some of the preceding sections must in fact be adiabatic rather than isothermal, because of failure to reach thermal equilibrium within the period of deformation. This distinction has usually been ignored, and reasonably so since the difference between the adiabatic and isothermal quantities is in most cases negligible. For the sake of completeness, however, some general features of the problem are mentioned here. 

Isothermal change of state at inlet stagnation temperature between the inlet stagnation pressure and zero pressure, where the gas behaves as ideal. 

Another isothermal change of state at nozzle throat temperature between the zero pressure and the pressure in the nozzle throat. 

During the reversible process the system undergoes a sequence of states all of which are infinitely near a true, thermodynamic equilibrium. Therefore, the reversible process can be unambiguously illustrated in a diagram, for example as a curve depicting a reversible isothermal change of state for a gas in a pV diagram. 

Conditions. We consider a reversible, isobaric and isothermal change of state transforming the system from water into water vapour... 

According to Joule s law (3.19), the internal energy U of ideal gas is solely a function of the gas temperature U = U T). For an isothermal change of state with ideal gas, this means that dT, and thereby dU, is zero. Prom the first law (3.2) we then get... 

For an isothermal change of state of ideal gas, the sum of the supplied heat <5i.2 and the work done W12 is zero. 

For a reversible and isothermal change of state (1) (2) with an ideal gas, the volume work done on the system can be determined by... 

Note The assumption of a reversible, isothermal change of state is necessary for a unique calculation of the volume work W12 done, since the work W is not a state function. However, as state functions, AU and AH, are independent of the process path. 

Isothermal process. Generally, for an isothermal change of state with... 

Specifically, for a reversible, isothermal change of state with an ideal gas... 

The ratio Q3/Q1) is solely determined by the ratio between the temperatimes T3 and Ti in the two heat reservoirs this can be seen by introduction of the previously derived expression for Q by an isothermal change of state with an ideal gas (3.27)... 

Figure 4.13. In a reversible, isothermal change of state with an ideal gas the internal energy U is constant the supplied heat Q corresponds to the work performed by the gas on its surroundings. In this case, AS can be calculated from the equation of definition.

Assume a system containing n mol of an ideal gas at the temperature T (K). By a reversible, isothermal change of state of the gas, the reversibly supplied heat Qrev according to (3.27) will be determined by... 

Thus, in conclusion, we have the following expression for calculation of the entropy change AS for isothermal changes of state with ideal gases... 

Once more it shall be noted that although AS has been determined for a reversible, isothermal change of state, (4.22), it also applies to an arbitrary reversible or irreversible change of state between the specified states of equilibrium (1) and (2) this is a consequence of the fact that the entropy 5 is a state function. Generally, the entropy S of gases increases with increasing dilution, i.e. when the volume Y is increased or when the pressure p is reduced. This is because the entropy 5 is a measure of the degree of disorder at molecular level. As will be seen in section 4.10, the molecular disorder, and thus the entropy, increases when crystalline substances melt and when liquids evaporate - i.e. by phase transformations that lead to increased disorder at molecular level. 

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