Free (unrestrained) expansion of an ideal gas:\nWhy does no cooling occur during the unrestrained expansion of an ideal gas?

Introduction / Context:
Free (Joule) expansion is an important thought experiment in thermodynamics: a gas expands into a vacuum without doing external work and without heat exchange. Understanding why an ideal gas does not cool (its temperature remains unchanged) in this process requires recognizing the ideal gas model assumptions about intermolecular forces.

Given Data / Assumptions:

• Ideal gas model: no intermolecular forces; internal energy depends only on temperature.
• Unrestrained expansion into a vacuum: W = 0 (no external work), Q = 0 (adiabatic), instantaneous process.
• No phase change and no kinetic/potential energy changes of the bulk system.

Concept / Approach:
For an ideal gas, internal energy U is a function only of temperature (U = U(T)). In a free expansion, Q = 0 and W = 0, so ΔU = 0. Therefore, ΔT = 0. Real gases can cool or warm in throttling (Joule–Thomson effect) due to intermolecular forces, but the ideal gas has none; hence there is no temperature change in free expansion.

Step-by-Step Solution:

Verification / Alternative check:
Compare to throttling (constant enthalpy). For an ideal gas, enthalpy also depends only on temperature, so throttling shows no temperature change either, reinforcing that intermolecular forces are required for temperature shifts.

Why Other Options Are Wrong:

• (a) and (b) misstate energy transfers; no external work is done and molecular collisions remain elastic but do not “offset work.”
• (c) Inversion temperature pertains to the Joule–Thomson effect for real gases, not free expansion of an ideal gas.

Common Pitfalls:
Confusing free expansion (Q = W = 0) with throttling or polytropic expansions; assuming temperature must drop simply because volume increases.

Final Answer:
Molecules exert no intermolecular attractive forces on each other.