So in other words, dU = mCvdT - PdV, I know what the dT term is and if I guessed a PdV I would know what dU was but thats with a guessed PdV, instead of guessing you could solve explicitly for P by rearranging the equation. I guess you could use the tabulated dU from NIST but would that number necessarily stay constant if the volume were changing?Hi Ron,
Glad to hear the database worked out for you. As for how it works, to the best of my knowledge, there are simply a whole bunch of equations behind it that determine the various properties given the specific state of the fluid as that state is defined by 2 parameters. I guess it’s something like putting equations to all the data in steam tables.
Regarding how to incorporate the case of an expanding vessel (whether it’s just ‘stretching’ or you have a spring loaded piston or other way of removing work) that gets just a bit more tricky. I suppose such a case has application to things such as Sterling engines perhaps. At any rate, there has to be some way of determining the final state, be it final temperature or total heat transferred or some other parameter.
If I had to do this, I’d put a spreadsheet together and have an input so I could ‘guess’ at the final pressure. That guess at final pressure would go into determining total work removed from the system, be it from the vessel stretching or from a piston moving through some distance. Given the guess at pressure, one could then calculate the final volume (which determines final density) and work removed (Wout).
Now let’s say you have as a given, the total heat input. The first law now reduces to:
dU = Qin – Wout
You have Qin (a given) and now with the guess you made, you have Wout. At that point, you can calculate the final internal energy:
U2 – U1 = Qin – Wout
U2 = U1 + Qin – Wout
So now you have U2 and rho (remember that the guess at final pressure also gave you final volume so you have mass divided by volume) which gives you the final state.
The final state calculated from this will give you the final pressure which isn’t likely to match the final pressure that you guessed – but that doesn’t matter.
Now you have another block in your spreadsheet that finds the difference between the pressure you guessed and the pressure calculated from the above first law equation. That block should be 0 if you guessed correctly. So all you need to do now is use the solver to set that cell to 0 by changing the pressure you guessed at. When the pressure you guess at and the actual pressure calculated by the first law are the same, you’ve accurately calculated the final state, including the final volume of the vessel and work removed.