Adep change along isotherm (Eq.(6))

[mostafa-razavi]

@jrelliottoh @ramess101

Something bugs about Eq.(6) as defined below

The above equation is only true if rho_1=0, so this equation is wrong by itself. The reviewer will probably complain about it. Why not reformulating this section as follows

The above Eq.(6) is always true by itself even if rho_1 is not zero. We actually use this formula when numerically integrating along supercritical isotherm, so it has value by itself. Then we mention that in ITIC derivations we deal with rho1=0 along isotherms (supercritical isotherm and isotherm at Tsat on vapor side (Eq.8)) therefore LHS can be Adep(T,rho_2).

what do you guys think?

[ramess101]

@mostafa-razavi

So should we change Equation 5 such that it is Adep(T1,rho) - Adep(T2,rho)? It wouldn't make sense to have one in terms of Adep and one as A. Would that be fine?

[ramess101]

@mostafa-razavi

Is there a more general version of Equation 6 that is true even if rho1 != 0?

[mostafa-razavi]

So should we change Equation 5 such that it is Adep(T1,rho) - Adep(T2,rho)? It wouldn't make sense to have one in terms of Adep and one as A. Would that be fine?

I think it makes sense because we are using Eq(5) as it is (in A form) in Eq(9)

Is there a more general version of Equation 6 that is true even if rho1 != 0?

[ramess101]

@mostafa-razavi

OK, then if we need to keep Eq 5 as A form, I would keep Eq 6 in the A form and just explicitly include \rho1 =0 in A(T,rho1=0) and the integrand (rho1=0 to rho2). Would that be correct?

[mostafa-razavi]

Is there a more general version of Equation 6 that is true even if rho1 != 0?

This equation might be correct:

A(T,rho2)/RT - A(T,rho1)/RT = Int_{rho_1}^{rho_2} Z/rho drho

But we don't use this form anywhere, so I don't want to use it.

[mostafa-razavi]

OK, then if we need to keep Eq 5 as A form, I would keep Eq 6 in the A form and just explicitly include \rho1 =0 in A(T,rho1=0) and the integrand (rho1=0 to rho2). Would that be correct?

That would be correct but it would lose its generality. On the other hand it would be consistent with Eq(5). I don't know

[ramess101]

A(T,rho2)/RT - A(T,rho1)/RT = Int_{rho_1}^{rho_2} Z/rho drho

Yeah I was wondering if that was correct. It seems right since A \propto PdV so A/RT = PdV/RT or Z/rho drho... but so I am confused how we get the Z-1/rho form inside the integrand, shouldn't the -1 term come out after integrating with the lower bound as rho1=0?

[mostafa-razavi]

... A \propto PdV so A/RT = PdV/RT or Z/rho drho ....

How is PdV/RT = Z/rho drho? Shouldn't it be Z/drho rho?

[ramess101]

If V= 1/rho, then dV = -1/rho^2 drho.

Z = PV/RT or P/rhoRT so Z/rho = P/rho^2RT and thus -PdV/RT (A propto negative PdV) is equal to Z/rho drho

On Wednesday, April 3, 2019, mostafa-razavi notifications@github.com wrote:

... A \propto PdV so A/RT = PdV/RT or Z/rho drho ....

How is PdV/RT = Z/rho drho? Shouldn't it be Z/drho rho?

— You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub https://github.com/mostafa-razavi/ITIC-paper/issues/44#issuecomment-479713493, or mute the thread https://github.com/notifications/unsubscribe-auth/AWUvhFAdvtVxIeE2AyPp__TkLSVoByxuks5vdVKvgaJpZM4cbnlu .

[mostafa-razavi]

@ramess101 we need to decide between these:

1)

2)

3)

[ramess101]

I think some feedback from Richard would be very helpful. Are each of these equations valid? I am somewhat confused where the -1/rho term comes from now.

On Wednesday, April 3, 2019, mostafa-razavi notifications@github.com wrote:

@ramess101 https://github.com/ramess101 we need to decide between these:

1.

[image: image] https://user-images.githubusercontent.com/16358113/55518866-a60a4800-5643-11e9-9d96-1247d21138d8.png

1.

[image: image] https://user-images.githubusercontent.com/16358113/55519001-26c94400-5644-11e9-91c8-3c28bec029da.png

1.

[image: image] https://user-images.githubusercontent.com/16358113/55523488-909f1900-5657-11e9-867c-c4116ec3d87d.png

— You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub https://github.com/mostafa-razavi/ITIC-paper/issues/44#issuecomment-479715738, or mute the thread https://github.com/notifications/unsubscribe-auth/AWUvhDWNqQPytgbl_05qXF7T1R0oFFHXks5vdVW9gaJpZM4cbnlu .

[mostafa-razavi]

@jrelliottoh @ramess101

I figured out an alternative path to derive the ITIC equations. The new path is longer but it's much simpler and more straightforward. Plus, it does not depend on different confusing types of departure function. I'm updating Section 2 and I'll send you the new manuscript when it's done.

[ramess101]

How different? I think it is risky to do a total rewrite at this point. Make sure to save the old version

On Thursday, April 4, 2019, mostafa-razavi notifications@github.com wrote:

@jrelliottoh https://github.com/jrelliottoh @ramess101 https://github.com/ramess101

I figured out an alternative path to derive the ITIC equations. The new path is longer but it's much simpler and more straightforward. Plus, it does not depend on different confusing types of departure function. I'm updating Section 2 and I'll send you the new manuscript when it's done.

— You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub https://github.com/mostafa-razavi/ITIC-paper/issues/44#issuecomment-479858590, or mute the thread https://github.com/notifications/unsubscribe-auth/AWUvhGmXv-xuui4aqD1cpokQr44rtNmQks5vdeFPgaJpZM4cbnlu .