compressibility

Question

Isothermal compressibility κ is defined as?

RankGuru · Accepted Answer

1. **Definition**: Compressibility ($\kappa$) is a measure of how much a volume of matter decreases when placed under pressure.
2. **Math form**: It is the fractional change in volume per unit change in pressure at constant temperature.
3. **Equation**: **$\kappa = -\frac{1}{V} \left(\frac{\partial V}{\partial P}\right)_T$**.
4. **Sign Reason**: Since volume decreases ($\partial V < 0$) as pressure increases ($\partial P > 0$), the partial derivative is negative. The leading minus sign ensures $\kappa$ remains a positive quantity.

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compressibility

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