Free expansion (Joule expansion) of an ideal gas: A rigid, perfectly insulated container of volume V is split into two equal halves. One side is vacuum; the other contains 1 mol ideal gas at 298 K. After the partition is broken, what is the final temperature of the gas?

Introduction / Context:
Free expansion into vacuum (Joule expansion) is a classic thermodynamics scenario used to distinguish ideal from real gas behavior. It illustrates how internal energy depends on temperature for an ideal gas.

Given Data / Assumptions:

• Rigid container (no boundary work).
• Perfectly insulated (adiabatic: Q = 0).
• Ideal gas with temperature-independent heat capacity.
• Initial T = 298 K; final volume doubles after partition removal.

Concept / Approach:
First law for a closed, adiabatic, rigid system: ΔU = Q − W = 0 − 0 = 0. For an ideal gas, U depends only on T. Therefore ΔT = 0 and the final temperature equals the initial temperature.

Step-by-Step Solution:

Verification / Alternative check:
Real gases may show small Joule effects due to non-ideal interactions, but the ideal-gas model assumes zero; thus, temperature remains unchanged.

Why Other Options Are Wrong:

• Greater/Less than 298 K: Would require net heat or work interactions, absent here, or non-ideal effects not assumed.
• Cannot be determined: It can, from the first law and ideal-gas property of U(T) only.

Common Pitfalls:
Confusing free expansion with throttling (Joule–Thomson) where enthalpy, not internal energy, is constant and real-gas effects matter.

Final Answer:
298 K