Question

Define Extensive property. Calculate the work done during the expansion of 2 moles of an ideal gas from 10 dm\(^3\) to 20 dm\(^3\) at 298 K in vacuum.

Hint:

In free expansion (in vacuum), no work is done since \( P_{\text{ext}} = 0 \); extensive properties scale with system size.

Answer 1

Definition: An extensive property is a physical property of a system that depends on the amount or extent of the substance, such as mass, volume, or total energy.
Calculation of Work Done: For an ideal gas expanding in a vacuum (free expansion), external pressure \( P_{\text{ext}} = 0 \). Work done \( W = -P_{\text{ext}} \Delta V \).
\[ \Delta V = 20 \, \text{dm}^3 - 10 \, \text{dm}^3 = 10 \, \text{dm}^3 = 0.01 \, \text{m}^3. \] \[ W = -0 \cdot 0.01 = 0 \, \text{J}. \] Answer: Work done = 0 J.