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 to or from the system, so \(q = 0\) (no heat transfer).
• Free expansion: The gas expands into a vacuum, meaning there is no work done by the gas, so \(W = 0\).
• According to the First Law of Thermodynamics, which states that the change in internal energy is equal to the heat added to the system minus the work done by the system: \[ \Delta U = q + W = 0 \quad (\text{since both } q = 0 \text{ and } W = 0) \] Therefore, the change in internal energy is zero, implying no change in the temperature for an ideal gas.

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

• Temperature remains constant \(\Rightarrow\) Isothermal
• The process is not isobaric because the pressure of the gas changes during expansion.
• The process is not isochoric because the volume changes as the gas expands.
• It is not isoentropic because entropy increases in an irreversible process like free expansion.