Question

Isothermal compressibility is given by

• A. \( \frac{1}{V} \left( \frac{\partial V}{\partial P} \right)_T \)
• B. \( \frac{1}{P} \left( \frac{\partial P}{\partial V} \right)_T \)
• C. \( -\frac{1}{V} \left( \frac{\partial V}{\partial P} \right)_T \)
• D. \( -\frac{1}{P} \left( \frac{\partial P}{\partial V} \right)_T \)

Hint:

Isothermal compressibility measures the relative change in volume with respect to pressure at constant temperature.

Answer 1

The Correct Option is C

Step 1: Understanding isothermal compressibility.
Isothermal compressibility describes how the volume of a substance changes with pressure at constant temperature. It is defined as: \[ \beta_T = -\frac{1}{V} \left( \frac{\partial V}{\partial P} \right)_T \] where \( \beta_T \) is the isothermal compressibility, \( V \) is the volume, \( P \) is the pressure, and \( T \) is the temperature.
Step 2: Identifying the correct option.
The correct form of isothermal compressibility is \( \beta_T = -\frac{1}{V} \left( \frac{\partial V}{\partial P} \right)_T \), which matches option (C).