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Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which this textbook has been adopted.

Any other reproduction or translation of this work beyond that permitted by Sections or of the United States Copyright Act without the permission of the copyright owner is unlawful. The following table gives the values for the compressibility, enthalpy departure and the entropy departure along the saturated liquid-vapor boundary. These are used for all the problems using generalized charts as the figures are very difficult to read accurately consistently along the saturated liquid line.

It is suggested that the instructor hands out copies of this page or let the students use the computer for homework solutions. If you have experimental information about saturation properties down to a certain temperature Clapeyron equation will allow you to make an intelligent curve extrapolation of the saturated pressure versus temperature function Psat T for lower temperatures.

From Clapeyrons equation we can calculate a heat of evaporation, heat of sublimation or heat of fusion based on measurable properties P, T and v. The similar changes in entropy are also obtained since. From the definition and variation in Gibbs function, see Eq.

If I raise the pressure in an isentropic process, does h go up or down? Is that independent upon the phase?

The magnitude is proportional to v i. A compressibility factor that is greater than one comes from domination of intermolecular forces of repulsion short range over forces of attraction long range — either high temperature or very high density.

This implies that the density is lower than what is predicted by the ideal gas law, the ideal gas law assumes the molecules atoms can be pressed closer together. What is the benefit of the generalized charts? Which properties must be known besides the charts themselves?

The generalized charts allow for the approximate calculations of enthalpy and entropy changes and P,v,T behaviorfor processes in cases where specific data or equation of state are not known. They also allow for approximate phase boundary determinations. It is necessary to know the critical pressure and temperature, as well as ideal-gas specific heat. How can that be? This also means that these other forms of ice are all heavier than liquid water.

In the two-phase region, P is a function only of T, and not dependent on v. The slope is the same at a given T regardless of v. The slope becomes higher with higher T and generally is the highest near the critical point.

Sketch on a P-T diagram how a constant v line behaves in the compressed liquid region, the two-phase L-V region and the superheated vapor region? If I raise the pressure in an isothermal process does h go up or down for a liquid or solid? What do you need to know if it is a gas phase?

For a liquid or solid, v is much more sensitive to T than P. Most equations of state are developed to cover the gaseous phase, from low to moderate densities.

## Solucionario Fundamentos da Termodinamica Van Wylen 7ª ed Cap. 14

Many cover high-density regions as well, including the compressed liquid region. To cover a wider region the EOS must be more complex and usually has many terms so it is only useful on a computer.

In a two-phase region, P depends only on T. There is a discontinuity at each phase boundary.

### Solucionario Fundamentos da Termodinamica Van Wylen 7ª ed Cap. 14

It is actually difficult to determine the phase boundary from the EOS. However at very high P, the substance eventually must become a solid, which cannot be compressed to a volume approaching zero. It has been observed from experimental measurements that substances do behave in that ternodinamica. If an equation of state is to be accurate in the near-critical region, it would have to satisfy these two conditions.

### Solucionario Fundamentos da Termodinâmica Van Wylen 7ª ed Cap. 15

If the equation is simple it may be overly restrictive to impose fundsmentos as it may lead to larger inaccuracies in other regions. Departure terms for h and s are small at very low pressure or at very high temperature. In both cases, Z is close to 1 and this is the ideal gas region.

The departure functions vah h and s as defined are always positive. What does that imply for the real substance h and s values relative to ideal gas values?

In-Text concept questions a-f Study guide problems Clapeyron equation Enthalpy, internal Energy and Entropy Volume Expansivity and Compressibility Equations of State Generalized Charts Mixtures Helmholtz EOS Review problems Property Relations, Maxwell, and those for Excerpts from this work may be reproduced by instructors for distribution on a not-for-profit basis for testing or instructional purposes only to students enrolled in courses for which this textbook has been adopted.

Borgnakke and Sonntag The following table gives the values for the compressibility, enthalpy departure and the entropy departure along the saturated liquid-vapor boundary. Tags Termodinamica Van Wylen 7 ed.