Thermodynamics filled in class notes_Part_117

Thermodynamics filled in class notes_Part_117 - 7.1....

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 7.1. ISOTHERMAL, ISOCHORIC KINETICS 241 • Near the first non-physical root at ρ e O = − . 003, a positive perturbation from equi- librium induces f < 0, which induces d ρ O /dt < 0, so ρ O returns to its equilibrium. Similarly, a negative perturbation from equilibrium induces d ρ O /dt > 0, so the system returns to equilibrium. This non-physical equilibrium point is stable. Note stability does not imply physicality! • Perform the same exercise for the non-physical root at ρ e O = − . 000518944. We find this root is unstable . • Perform the same exercise for the physical root at ρ e O = 0 . 000442414. We find this root is stable . In general if f crosses zero with a positive slope, the equilibrium is unstable. Otherwise, it is stable. Consider a formal Taylor series expansion of Eq. (7.85) in the neighborhood of an equi- librium point ρ 3 O : d dt ( ρ O − ρ e O ) = f ( ρ e O ) bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright =0 + df d ρ O vextendsingle...
View Full Document

This note was uploaded on 11/26/2011 for the course EGN 3381 taught by Professor Park-sou during the Fall '11 term at FSU.

Page1 / 2

Thermodynamics filled in class notes_Part_117 - 7.1....

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online