Chemistry · THERMODYNAMICS

Examine the two \( p-V \) indicator diagrams shown in the figure for the compression of an ideal gas from volume \( V_i \) to \( V_f \). Which relationship correctly compares the magnitudes of work done in finite steps (shaded area in Fig. 5.5(b)) and infinite infinitesimal steps (shaded area in Fig. 5.5(c)) during compression?

1. \( |w_{\text{finite steps}}| < |w_{\text{infinite steps}}| \) because the area under the curve is always minimized in irreversible processes.
2. \( |w_{\text{finite steps}}| = |w_{\text{infinite steps}}| \) because work is a state function and the initial and final states are identical.
3. \( |w_{\text{finite steps}}| > |w_{\text{infinite steps}}| \) during compression because external pressure at each finite step must exceed internal pressure to cause compression, making the stepped area larger.
4. \( |w_{\text{finite steps}}| = 0 \) because finite step compression produces no net boundary displacement against external pressure.