CHM2104 Lecture 10 – Isothermal Compressibility & Joule–Thomson Effect

Isothermal compressibility (κT)

Measures how much volume changes with pressure at constant T.

Formula for κT

κT = -(1/V)(∂V/∂P)T.

Sign of κT

Always positive (volume decreases when pressure increases).

Units of κT

Pa⁻¹ or 1/Pressure.

Large κT value

Substance compresses easily (e.g., gas).

Small κT value

Substance resists compression (e.g., liquid, solid).

κT for ideal gas

1/P.

Joule

Thomson effect (μ) - Temperature change during adiabatic expansion through a valve or porous plug.

Formula for μ

μ = (∂T/∂P)H.

Positive μ

Gas cools during expansion.

Negative μ

Gas warms during expansion.

μ for ideal gas

0 (no cooling or heating).

Reason μ = 0 for ideal gas

No intermolecular forces → no conversion between KE and PE.

Reason gas cools on expansion

Molecules work against attractions → lose KE → T decreases.

Inversion temperature

Temperature where μ changes sign.

Above inversion temperature

Gas warms when expanding.

Below inversion temperature

Gas cools when expanding.

Real-life use of JT effect

Refrigeration, air conditioning, gas liquefaction.

Adiabatic expansion meaning

No heat exchange (q = 0).

κT meaning check

Shows compressibility at constant temperature.

JT summary

μ > 0 = cooling, μ < 0 = heating, μ = 0 = ideal gas.