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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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Thu, 26 Mar 2015 18:33:24 -0700

Planned Departure's function is simple but profound. It gives an individual control over their legacy, every minute nitty-gritty of their existence, to ensure that their wishes are carried out even when that person is no longer around to be able to ...

IBNLive

IBNLive
Sat, 07 Feb 2015 06:30:15 -0800

Such has been the frustration that Fikile Mbalula, South Africa's sports minister, asked the team not to "become a bunch of losers" at the departure function in Johannesburg a few days ago. Reacting to the comment, AB de Villiers, South Africa's One ...

ecomento.com

ecomento.com
Tue, 24 Mar 2015 04:37:30 -0700

The smartest way to make sure you get maximum range on cold days is to plug in your car and enable the “precondition for departure” function before you go to bed at night. The car will automatically start heating the battery 150 minutes prior to departure.
 
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Mon, 29 Dec 2014 16:22:30 -0800

I had a small departure function, which I actually hosted, in order that I could ensure that the people who were there were people I chose to be there. ELEANOR HALL: Even for someone who came in there to drive change it seems there's a lot of vengeance ...

indiatvnews.com (press release) (blog)

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Fri, 06 Feb 2015 20:52:30 -0800

... Africa captain A.B. de Villiers has diplomatically downplayed comments from his nation's Sports Minister who warned the Proteas not to be "a bunch of losers" at the Cricket World Cup. Minister Fikile Mbalula told players at a departure function ...
 
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I had a small departure function, which I actually hosted, in order that I could ensure that the people who were there were people I chose to be there. ELEANOR HALL: Even for someone who came in there to drive change it seems there's a lot of vengeance ...
 
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... 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 ...

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Tue, 11 Mar 2014 10:35:03 -0700

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