Question

In thermodynamic process for free expansion, select the 'WRONG' statement out of the following options.

• A. Free expansions are adiabatic expansions and there is no exchange of heat between system and environment.
• B. A free expansion can be plotted on a p-V diagram.
• C. There is no work done on the system or by the system.
• D. It is an instantaneous change and the system is not in thermodynamic equilibrium.

Hint:

A free expansion is not a quasi-static process, so it has no path on a p-V diagram.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
In free expansion, a gas expands suddenly into a vacuum. It is rapid and irreversible, so the gas passes through non-equilibrium states.

Step 2: Key Formula or Approach:
A p-V diagram shows only equilibrium states, so only quasi-static (slow) processes can be drawn as curves on it.

Step 3: Detailed Explanation:
Statement A is correct: the expansion is fast, so it is adiabatic and \(Q = 0\).
Statement C is correct: the gas pushes against vacuum, so no work is done by or on the system.
Statement D is correct: the change is instantaneous and the intermediate states are not in equilibrium.
Statement B says that a free expansion can be plotted on a p-V diagram. This is the wrong one. Only the initial and final states have well defined \(p\) and \(V\), and no curve joins them.

Final Answer:
The wrong statement is B, option (B). \[ \boxed{\text{B}} \]