Question

During the free expansion of an ideal gas, which of the following physical quantity remains constant

• A. Temperature
• B. Pressure
• C. Volume
• D. Ratio of pressure to volume

Hint:

Remember: Free expansion is neither reversible nor quasi-static. While $T_i = T_f$, the intermediate states are undefined, and the entropy of the system increases significantly.

Answer 1

The Correct Option is A

Free expansion occurs when a gas expands into a vacuum within an insulated container. We analyze this using the First Law of Thermodynamics. 1. Work Done ($W$): Since the gas expands against a vacuum (zero external pressure), no work is done by the gas: $W = 0$.

2. Heat Exchange ($Q$): Free expansion is typically an adiabatic process in a perfectly insulated system, meaning no heat enters or leaves: $Q = 0$.

3. Internal Energy ($U$): According to the First Law, $\Delta U = Q - W$. Since both $Q$ and $W$ are zero, $\Delta U = 0$. The internal energy remains constant.

4. Temperature ($T$): For an

ideal gas, internal energy is a function of temperature only ($U \propto T$). Because internal energy does not change, the

temperature remains constant. This process is isothermal, though not through heat exchange but through the nature of the expansion itself.