digplanet beta 1: Athena
Share digplanet:

Agriculture

Applied sciences

Arts

Belief

Chronology

Culture

Education

Environment

Geography

Health

History

Humanities

Language

Law

Life

Mathematics

Nature

People

Politics

Science

Society

Technology

In thermodynamics, a departure function is defined for any thermodynamic property as the difference between the property as computed for an ideal gas and the property of the species as it exists in the real world, for a specified temperature T and pressure P. Common departure functions include those for enthalpy, entropy, and internal energy.

Departure functions are used to calculate real fluid extensive properties (i.e. properties which are computed as a difference between two states). A departure function gives the difference between the real state, at a finite volume or non-zero pressure and temperature, and the ideal state, usually at zero pressure or infinite volume and temperature.

For example, to evaluate enthalpy change between two points h(v1,T1) and h(v2,T2) we first compute the enthalpy departure function between the v1 and infinite volume at T=T1, then add to that the ideal gas enthalpy change due to the temperature change from T1 to T2, then subtract the departure function value between v2 and infinite volume.

Departure functions are computed by integrating a function which depends on an equation of state and its derivative.

## General Expressions

General Expressions for the Enthalpy H, the Entropy S and the Gibbs Energy G are given by[1]

$\frac{H^\mathrm{ig}-H}{RT} = \int_V^\infty \left[ T \left(\frac{\partial Z}{\partial T}\right)_V \right] \frac{\mathrm{d}V}{V} + 1 - Z$
$\frac{S^\mathrm{ig}-S}{R} = \int_V^\infty \left[ T \left(\frac{\partial Z}{\partial T}\right)_V - 1 + Z\right] \frac{\mathrm{d}V}{V} - \ln Z$
$\frac{G^\mathrm{ig}-G}{RT} = \int_V^\infty (1-Z) \frac{\mathrm{d}V}{V} + \ln Z + 1 - Z$

## Departure functions for Peng-Robinson equation of state

The Peng-Robinson equation of state relates the three interdependent state properties pressure P, temperature T, and molar volume Vm. From the state properties (P, Vm, T), one may compute the departure function for enthalpy per mole (denoted h) and entropy per mole (s)[2]:

$h_{T,P}-h_{T,P}^{\mathrm{ideal}}=RT_C\left[T_r(Z-1)-2.078(1+\kappa)\sqrt{\alpha}\ln\left(\frac{Z+2.414B}{Z-0.414B}\right)\right]$
$s_{T,P}-s_{T,P}^{\mathrm{ideal}}=R\left[\ln(Z-B)-2.078\kappa\left(\frac{1+\kappa}{\sqrt{T_r}}-\kappa\right)\ln\left(\frac{Z+2.414B}{Z-0.414B}\right)\right]$

Where $\alpha$ is defined in the Peng-Robinson equation of state, Tr is the reduced temperature, Pr is the reduced pressure, Z is the compressibility factor, and

$\kappa = 0.37464 + 1.54226\;\omega - 0.26992\;\omega^2$
$B = 0.07780\frac{P_r}{T_r}$

Typically, one knows two of the three state properties (P, Vm, T), and must compute the third directly from the equation of state under consideration. To calculate the third state property, it is necessary to know three constants for the species at hand: the critical temperature Tc, critical pressure Pc, and the acentric factor ω. But once these constants are known, it is possible to evaluate all of the above expressions and hence determine the enthalpy and entropy departures.

## References

• ^ Poling, Prausnitz, O'Connell: The Properties of Gases and Liquids, 5th Ed., McGraw-Hill, 2001. p. 6.5.
• ^ Kyle, B.G.: Chemical and Process Thermodynamics, 3rd Ed., Prentice Hall PTR, 1999. p. 118-123.

## Correlated terms

Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Departure_function — Please support Wikipedia.
A portion of the proceeds from advertising on Digplanet goes to supporting Wikipedia.
 54253 videos foundNext >
 Departure functionsDifference between real and ideal gas properties. Departure Function: van der Waals FluidDiscusses the enthalpy departure function for van der Waals fluid. Made by faculty at the University of Colorado Boulder, Department of Chemical and Biologic... Departure Entropy (Review)Calculates the departure entropy for a real gas. Made by faculty at the University of Colorado Boulder, Department of Chemical and Biological Engineering. Ch... Enthalpy Departure Function for Throttle FeedUse the exit conditions from a throttle to determine the enthalpy departure function for the inlet fluid. Made by faculty at the University of Colorado Bould... Shree Swaminarayan Mahotsav - UK (Function in India before departure) - 2010Swaminarayan UK London Oldham Satsang "Lalji Maharaj" Vadtal Temple "August 2010" 2010. Demo: SITA Horizon Departure ControlLearn more: http://www.sita.aero/horizon SITA Horizon Departure Control System is a core function of our next-generation Horizon Passenger Services System. I... Honda Lane Departure Warning (LDW)In this Tech Tidbit / Feature Function video, Angelo Marino shows us how the all new Honda Lane Departure warning (LDW) works. For further information, pleas... Vico-WF1 LDWS-Line Departure Warning System WWW.BEBUTTON.COM Londonhttp://www.bebutton.com/ LDWS -- Lane Departure Warning System Vico-WF1 has built-in LDWS. With the voice notice, Vico-WF1 will remind the driver of lane dep... Night Rider, different departure points, one destination? (français)Check out the advantages of the new Multiple-Pickup function. Night Rider: even more practical, even more for your money, even more sociable. Watch our new s... Prosecutor calls Pistorius' version of night Steenkamp died a 'lie' - court departureApril 10, 2014 - A prosecutor hammered at Oscar Pistorius's credibility at his murder trial on Thursday, asserting that the star athlete had a string of unli...
 54253 videos foundNext >

We're sorry, but there's no news about "Departure function" right now.

 Limit to books that you can completely read online Include partial books (book previews) .gsc-branding { display:block; }

Oops, we seem to be having trouble contacting Twitter