Question

Adiabatic free expansion of an ideal gas must be: \} \begin{tabular}{ll} (A) Isobaric & (B) Isochoric
(C) Isothermal & (D) Isoentropic
\end{tabular}

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

Hint:

Key points summarizing the principles Key Points: In free expansion, no work is done on or by the system ($W=0$). An adiabatic process means no heat is exchanged with the surroundings ($q=0$). For an ideal gas, the internal energy depends only on temperature ($\Delta U \propto \Delta T$), so no change in internal energy implies no temperature change. Entropy increases in a free expansion process, making it irreversible and not isoentropic. A special case of this phenomenon is the Joule expansion, which demonstrates the temperature constancy in an adiabatic free expansion.

Answer 1

The Correct Option is C

For an ideal gas undergoing adiabatic free expansion:

• Adiabatic: This means there is no heat transfer, so \(q = 0\).
• Free expansion: The gas expands into a vacuum, so no work is done, thus \(W = 0\).
• According to the First Law of Thermodynamics, the change in internal energy equals heat added minus work done: \[ \Delta U = q + W = 0 \quad (\text{since } q = 0 \text{ and } W = 0) \] Therefore, the change in internal energy is zero, leading to no temperature change for an ideal gas.

For an ideal gas, internal energy \(\Delta U\) depends only on temperature: \[ \Delta U = 0 \Rightarrow \Delta T = 0 \]
Thus, the temperature remains constant, indicating an isothermal process.

• Temperature remains constant \(\Rightarrow\) Isothermal
• The process is not isobaric because the pressure changes.
• The process is not isochoric because the volume changes.
• It is not isoentropic because entropy increases during this irreversible process.