Integral constant for internal energy of ionic liquid

[hosein]

Integral constant for internal energy of ionic liquid

I have a question, and I will be really grateful if someone helps me. I have a polynomial equation for internal energy which I calculated by integration an equation of state formula, which is based on density. But, because I calculated this using integration one integration constant which is temperature dependent( based on other articles) that I don't know how can I formulate it to have its magnitude to calculate internal energy at other range of data. My simulation box has contained 200 molecules of ionic liquid with one negative ion( PF6) and a positive one( butyl methyl imidazolium). Because according to internal energy equation at zero density internal energy is equal to the integration constant, we considered it as ionic liquid internal energy at ideal gas state. With all those in mind, how can I use a degree of freedom of rotational, vibrational, and translational to formulate this integration constant dependent of temperature to use it in other range of data? Or, is there any other method to formulate it? Thanks very much in advance

 

[HAYAO]

Are you doing a MD simulation? I don't know much about MD simulations.

I believe this deserves a new thread.

 

[hosein]

yes,
it is an MD simulation, but the simulation is not the problem it is more of a thermodynamic question

 

[HAYAO]

It would be nice if you can provide us with exactly which equation of state (which model) you are using.

 

[hosein]

Sure Hayao,
Ein=RT[(e(T)/2)*rho^2+ f(T)*rho + (g(T)/4)*rho^4]+ F(T)
e(T), f(T), and g(T) are coefficients of equation of state which I calculate Ein from.
F(T) is the integration constant

 

[HAYAO]

Sure Hayao,
Ein=RT[(e(T)/2)*rho^2+ f(T)*rho + (g(T)/4)*rho^4]+ F(T)
e(T), f(T), and g(T) are coefficients of equation of state which I calculate Ein from.
F(T) is the integration constant

I'm sorry, I do not know the density formulation of Equation of State. I always thought of it as an equation with pressure, volume, and temperature as variables, not in the form of internal energy, temperature, and density.

It would be nice if you could provide me the original equation and where it came from.Also, if this is a thermodynamics question, then I really think a new thread should have been made. This is quite off-topic from what this thread is about. I wonder if you can ask one of the moderators to split the thread (if that is even possible).

 

[hosein]

ok, let me complete the question, then I will make a new thread with all data.
([Zth + Zin] - 1)V^2 = e +f/rho+ g*rho^2
in=internal
th=thermal
Z=compressibility factor
(Zth - 1)V^2 = eth +fth/rho+ gth*rho^2
(Zin)V^2 = ein +fin/rho+ gin*rho^2

Ein =∫Pin/rho^2 drho+ F(T) = RT[(ein(T)/2)*rho^2+ fin(T)*rho + (gin(T)/4)*rho^4]+ F(T)
F(T)?

 

[Borek]

discussion continues here: https://www.physicsforums.com/threads/integral-constant-for-internal-energy-of-ionic-liquid.923093/