In Friday's lecture, we finished our uberproblem, obtaining expressions for q, w, ∆U and ∆H for the following reversible ideal gas processes: isobaric, isochoric, isothermal and adiabatic. Not only are the equations themselves useful, they demonstrate something that had previously been simply asserted, that q and w are path-dependent while ∆U and ∆H are not. We also saw (for the second time this quarter) the connections between U and constant-volume and H and constant-pressure conditions.
It is important, however, to realize that these results are secondary to the calculation process itself. That is, what we get as the answer is somewhat less important than how we get it. Though we are focusing on the ideal gas as our system, the logic underlying these calculations apply just as readily to real gases and other substances, though the actual mathematics will be a bit messier.
We also developed some mathematical relations important to adiabatic processes and saw how the heat capacity ratio naturally arises in those equations, which tie together two of the three simultaneously changing variables (P, V, T).
On Monday, a new homework set [hw.3] as we venture into Chapter 3 and its elegant elegance.