Free expansion of a gas (against vacuum): In classical thermodynamics, consider a free expansion where a gas initially confined by a partition expands into a vacuum after the partition is removed. For this process, the boundary (p*dV) work done by the system is ________.

Introduction / Context:
A free expansion is a classic thought experiment in thermodynamics. A gas suddenly expands into a vacuum with no opposing external pressure. Understanding why the boundary work term is zero clarifies differences between work, heat, and changes in internal energy, and prevents common misconceptions about “expansion implies work”.

Given Data / Assumptions:

• Initial gas in one chamber; the other chamber is vacuum.
• Partition removed; expansion is rapid and unresisted.
• No external pressure opposing the expansion (p_ext = 0).
• Closed system; no shaft work, no moving boundary against resistance.

Concept / Approach:
Boundary work is defined as W_b = ∫ p_ext * dV. In free expansion, the external pressure p_ext equals zero throughout the expansion, so the integral gives zero independent of the change in volume or temperature. Internal energy may still change if heat exchange occurs with the surroundings, but for an ideal gas in an insulated container the internal energy (and temperature) remain the same.

Step-by-Step Solution:

Verification / Alternative check:
A paddle wheel doing work or a resisting piston would be required for nonzero boundary work. Neither exists here; hence zero work is consistent with the definition and experiments.

Why Other Options Are Wrong:

• False: Contradicts W_b definition.
• Only for ideal gases: Incorrect; the integral uses external pressure, not gas model.
• Zero only if temperature stays constant: Temperature behavior is irrelevant to W_b in free expansion.

Common Pitfalls:
Confusing “gas expands” with “system does work”. Work requires an opposing force; vacuum provides none.

Final Answer:
True