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Expression for Pressure-volume (PV) Work

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Estimated time: 4 minutes
Maharashtra State Board: Class 12

Key Points: Expression for Pressure–Volume (PV) Work

Work in Isothermal Reversible Process

\[W_{rev}=-2.303nRT\log_{10}\frac{V_2}{V_1}\]

Or equivalently using Boyle's law (at constant T):

\[W_{rev}=-2.303nRT\log_{10}\frac{P_1}{P_2}\]

Where: n = number of moles; R = gas constant; T = absolute temperature (K); V₁, V₂ = initial and final volumes; P₁, P₂ = initial and final pressures.

Work in Isothermal Irreversible Process:

 

W = −Pext(V2 − V1)

 

  • Expansion: ΔV > 0 → W_expansion is positive (work done by system → negative sign)

  • Contraction: ΔV < 0 → W_contraction is positive

Work in Free Expansion-

When a gas expands into a vacuum (Pext = 0): W = 0

No work is done, regardless of whether the process is reversible or irreversible.

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