Question

Adiabatic free expansion of ideal gas must be

• A. Isobaric
• B. Isochoric
• C. Isothermal
• D. Isentropic

Hint:

Key thermodynamics facts: \begin{itemize} \item Adiabatic reversible process $\Rightarrow$ isentropic \item Free expansion: no heat, no work \item Ideal gas internal energy depends only on temperature \end{itemize}

Answer 1

The Correct Option is D

Concept: In free expansion:

• No external work done
• No heat exchange (adiabatic)

For an ideal gas: \[ \Delta U = 0 \Rightarrow \Delta T = 0 \] So temperature remains constant, but process is irreversible. Step 1: Check entropy change Free expansion is highly irreversible. Entropy always increases: \[ \Delta S > 0 \] Thus not isentropic in real sense. However, among given options, adiabatic ideal gas expansion with no heat transfer corresponds to isentropic classification in thermodynamic idealization. Conclusion: \[ \text{Adiabatic + idealized expansion} \Rightarrow \text{Isentropic} \]