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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[edit]

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[edit]

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[edit]

  • ^ 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[edit]


Original courtesy of Wikipedia: http://en.wikipedia.org/wiki/Departure_function — Please support Wikipedia.
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16 news items

 
Airport World Online
Thu, 16 Oct 2014 06:41:15 -0700

In-town check-in also increases departure function capacity and relieves potential congestion at the airport's check-in desks. In Hong Kong, a culture that places tremendous value on convenience and speed, the express train and in-town check-in ...

automotive.com

automotive.com
Tue, 11 Mar 2014 10:35:03 -0700

Standard features on the 2014 Honda Civic Si include a new 7-inch touchscreen with smartphone-like swiping features, push button smart, expanded view driver's mirror, and lane departure function. Honda has upgraded this model for the current model year.
 
The Lawyer
Wed, 28 Mar 2012 07:29:48 -0700

It takes just 5 minutes to register. Answer a few simple questions and once completed you'll have instant access. Register now. Why register to The Lawyer. Industry insight. In-depth, expert analysis into the stories behind the headlines from our ...
 
Chicago Tribune
Sat, 08 Oct 2011 01:03:45 -0700

... as long as the camera eye is unobstructed by something like snow or mud. The area is kept clear by the windshield wipers. The camera searches for other vehicles in its forward collision warning function and for lane markings in its lane departure ...
 
Forbes
Thu, 08 Mar 2012 07:17:13 -0800

The lane departure function was useful upstate where people practice cutting off as sport — a subtle beep and then the system shuts up. Five Days Later: To add some nature to our weekend, we headed for Stone Barn Center in Tarrytown. It was a very ...
 
Sydney Morning Herald
Fri, 14 Jun 2013 04:30:12 -0700

Usman Khawaja, wanting to rid management of the view he has a poor attitude, said only last month at the official team departure function in Sydney that he was not understood by ''new'' people in the team hierarchy. Beneath that here are undoubted ...
 
AutoGuide.com
Fri, 15 Jun 2012 09:58:29 -0700

The lane departure function is helpful,but experienced drivers will probably prefer to turn it off and avoid the annoyin alerts. This is, after all, a compact crossover and not a truck. As for the forward collision alert (FCA) feature, it doesn't ...
 
Indian Express
Mon, 25 Jun 2012 15:02:27 -0700

The venue here is Naushad Khan's new residence, where the burly left-arm pacer is among the special invitees for the departure function arranged for his mentor's eldest son, Sarfaraz, who is on his way to England. With everyone from local politicians ...
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