Physics · Ch 8 — Heat and Thermodynamics
PV Diagram for a Cyclic Process
PV Diagram for a Cyclic Process
On a P-V diagram, a cyclic process traces a closed loop (Figure 8.39), and the net work done over one complete cycle equals the area enclosed by that loop. Splitting the loop into an expansion leg (work done BY the gas, the larger shaded area under the "upper" path) and a compression leg (work done ON the gas, the shaded area under the "lower" path) (Figure 8.40), the net work is , which geometrically is the thin sliver of area actually trapped between the two paths (Figure 8.41) -- never simply the sum of the two individual areas. If the loop is traced clockwise, the net work done is positive (net work is done BY the system, since the higher-pressure expansion leg dominates); if traced anticlockwise, the net work is negative (net work is done ON the system). Example 8.22 wor …
What this figure shows. A closed loop on a P-V diagram made of two curved segments joining the same two states A(P1,V1) and C(P2,V2): an upper path through an intermediate point B representing an expansion leg from V1 to V2, and a lower path through an intermediate point D representing a compression leg back from V2 to V1, together forming one full closed …
What this figure shows. Two panels reusing the same closed A-B-C-D loop as Figure 8.39. Panel (a) shades only the area under the upper expansion path C-B-A (from V1 to V2), representing the work W1 done BY the gas during the expansion leg. Panel (b) shades only the area under the lower compression path A-D-C (from V2 back to V1), representing the work W2 done ON the gas during the compression leg. Comparing the two shaded areas visually sets up why the NET work in the full cycle is the difference between them, n …
What this figure shows. The same closed A-B-C-D loop as Figures 8.39-8.40, but this time with only the thin region actually enclosed between the upper (expansion) and lower (compression) paths shaded in green -- representing the net work done in the complete cycle, W1 minus W2. The figure makes clear that the net work is not the full area under either individual curve, but specifically the sliver of area trapped between the two curves that make up the closed loop, and that this net value can be positive (loop traced clockwise) or negative (loop …