Ok, first I would like to say that my derivation of q was wrong. Sorry but I am only in AP Chemistry and I thought I could modify the first law of thermodynamics and the equation for Enthalpy to fit your situation.
After struggling with your problem I finally took it to my teacher and what he said we would have to do is quite difficult.
Now, I am unsure of your background but I am sure of mine
. I haven't taken Calculus yet but according to my teacher it involves principles used in physics that involve calc-applied math.
This is what he said to do.
First of all . . .
I was right in that . . .
isothermal process ?E=0 b/c T is proportional to internal E of system in isothermal process
I was not correct in my modification of work . . . here is why
?E = q + w
0 = q + w
q = -w
in the 2 last lines, you can't make the assumption that volume is changing because you do not know the volume and that one can't use this enthalpy formula for a changing volume and changing pressure at the same time. This formula can only be utilized when pressure is constant.
To account for a changing volume, it becomes more involved:
First of all, you use the ideal gas law equation to find the two different volumes
then once you find the two volumes, you plug it into P?V (constant pressure)
he comes the tough party (for me at least)
then you use this equation to determine the amount of energy = work performedw/n = RT (integrate symbol w/ superscript Vf and subscript Vi) dv / V = RT ln Vf/Vi
R will be 8.314 and T will be in kelvins, n = moles
use the two volumes you found and plug it into the equation above
this should enable you to find what you're looking for . . . although I don't know how to use integrals yet so GOOD LUCK!
Please will other MEMBERS EVALUATE THE METHOD I USED!