This is a BEAUTIFUL explanation. Wow ! Thank you, Chet. I've learned a LOT already from you in this thread and there is still more to go :)
Is there a mathematical generalization behind this ? Or, it depends upon a particular situation, like this case?
I am afraid I don't follow your insight here...
Secondly, this is not obvious to me. why you compare two reversible processes C and D instead of compare processes E, C (or D) and irreversible...
I was trying to plot the process E on the P-V diagram and calculate the area to see how it compared with other reversible processes (A-D). I will try this on my own and ask you if I don't make any headway.
On a side note: I am trying to read a J.Chem.Edu article (attached) on 1st law. I hope...
Thanks. Typo in my calculation:
1. (P0,T0,V0) to (Pa, T0/4, Vo) where Pa = P0/4
2. (Pa, T0/4, Vo) to (Pb,T0/4, V1) where Pb* V1 = Pa * V0 = nRT0/4
3. (Pb,T0/4, V1) to (P1,T1, V1) where Pb = (P1/T1) * (T0/4)
Dimensionless work, W/nRT0 = 0.25* ln(V1/V0) = W( for path C) /4. This is less than W(irrev).
How did you came up with this example, I wonder? I don't mean to disrupt your flow of thought (so you can check the question below, when you see fit):
Another question: I tried to chart this process...
I can't prove that this holds in general but I think that reversible paths produce more work than irreversible as in the reversible case, the entire area under the path connecting initial and final states is used. I need to think more about it, though !
Thanks, this is what I have, BUT the calculations for processes C and D would change depending on your clarification for the question I had asked earlier.
PROCESS C
1. Isothermal expansion at temperature To from Vo to V1
2. Isochoric cooling at volume V1 from To to T1
I got this for W(total)= RT0ln(V1/V0). For the overall process, V1/V0 = (Po/P1) * (T1/T0). For the 1st step,V1/V0 = (Po/P1) . Since work for step 2 =0, W(total) = W1, hence I used...
There was a typo in the sign (sigh!) in calculations for process A. Apologies for the delay, I have started to use Freeoffice and not excel, so things took time to figure out.
I have attached my working and the stacked graphs. Thanks and have a good weekend.
I didn't follow your remark on the logarithms. I used log(po/p1) for the X-coordinate.
I reworked the calculations. Seems I was using the sign convention for W and Q followed in chemistry which is opposite to that followed in engineering !