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1.6

Resisting pressure-vacuum

The pressure in mechanical work or P-V work

The magnitude of mechanical work or the P-V work is the force F, multiplied by the displacement dx through which the system boundary moved

\[\delta W=F\quad dx\\ F=\bar { P } \cdot A\\ \delta W=\bar { P } \cdot Adx=\bar { P } \cdot dV\]

\(\blacklozenge\) Be careful! The pressure \(\bar { P }\) here is the “resisting” pressure, NOT the system pressure P.

If your system is a gas with pressure P, and it expands against vacuum by volume ΔV, work done by the system is “ZERO” since the resisting pressure is zero

$$ \delta W=-\bar { P }\quad dV=0 $$

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Thermodynamics in Energy Engineering

Hanyang University