Question

In case of free expansion, which one of the following statements is WRONG ______.

• A. It is an instantaneous change.
• B. The system is not in thermodynamic equilibrium.
• C. Free expansion can be plotted on a P-V diagram.
• D. It is an uncontrolled change.

Hint:

To draw any line on a P-V graph, you must know the exact pressure at every millisecond. In explosions or free expansions, the gas is in chaotic turmoil, making a single defined "Pressure" impossible to measure!

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
The question asks us to identify the factually incorrect statement regarding the thermodynamic process known as "free expansion".

Step 2: Detailed Explanation:
Free expansion occurs when a gas is allowed to expand into an empty, evacuated space (a perfect vacuum).
Let's evaluate the thermodynamics of this specific process:
- Because the gas expands into a vacuum, there is zero external opposing pressure ($P_{\text{ext}} = 0$).
- Therefore, the mechanical work done by the gas is strictly zero ($W = P_{\text{ext}} \Delta V = 0$).
- The process is typically extremely rapid and adiabatic, meaning there is no time for heat transfer ($Q = 0$).
- Since $Q = 0$ and $W = 0$, the internal energy change is zero ($\Delta U = 0$).
Let's look at the given statements:
- (a) Instantaneous change: It is extremely rapid. (Generally considered true in context).
- (b) Not in equilibrium: Because the expansion is violent, rapid, and completely unresisted, extreme turbulence and pressure gradients exist inside the gas. It is a highly irreversible process, meaning intermediate states are strictly NOT in thermodynamic equilibrium. (True).
- (d) Uncontrolled change: Since there is no opposing piston or pressure to balance against, the expansion cannot be slowed down or reversed. (True).
- (c) Plotted on a P-V diagram: A P-V diagram can only be drawn as a continuous curve if every single intermediate state during the process is in perfect thermodynamic equilibrium (a quasi-static, reversible process). Because free expansion is highly turbulent and non-equilibrium, it does not possess defined uniform pressure or temperature values during the transition. Therefore, it is physically impossible to plot the path of a free expansion on a P-V diagram (only the isolated initial and final dot states can be marked). This statement is heavily WRONG.

Step 3: Final Answer:
The wrong statement is that free expansion can be plotted, matching option (c).