Question

For an ideal gas, coefficient of volume expansion is given by

• A. \( \frac{1}{p} \)
• B. \( \frac{1}{pV} \)
• C. \( \frac{1}{R} \)
• D. \( \frac{1}{T} \)

Hint:

For ideal gases, volume expansion coefficient \( \beta = \frac{1}{T} \), showing inverse dependence on temperature.

Answer 1

The Correct Option is D

Coefficient of volume expansion \( \beta \) is defined as: \[ \beta = \frac{1}{V} \cdot \left( \frac{\partial V}{\partial T} \right)_P \] For ideal gas: \[ PV = nRT \Rightarrow V = \frac{nRT}{P} \Rightarrow \frac{\partial V}{\partial T} = \frac{nR}{P} \] \[ \beta = \frac{1}{V} \cdot \frac{nR}{P} = \frac{1}{\frac{nRT}{P}} \cdot \frac{nR}{P} = \frac{1}{T} \]