A tank is divided into two compartments with one compartment containing a gas at a given pressure, while the second is completely evacuated. If the partition is removed, the gas occupies the entire compartment. Which one of the following statements is CORRECT?
Show Hint
- Work done is equal to the area under the curve of a \(p-V\) diagram
- Expansion of gas is not restrained by external force
- The entire process is reversible
- The overall change in volume is zero for the entire system
The Correct Option is B
Solution and Explanation
The given process is the sudden removal of a partition, where gas expands into a vacuum. This is known as a free expansion process.
Step 2: Characteristics of free expansion.
- No external force opposes the expansion. - No work is done: \(W = 0\). - No heat interaction if the system is insulated. - The process is irreversible.
Step 3: Check options.
(A) Incorrect – Work done is not equal to the \(p-V\) area, in fact \(W = 0\).
(B) Correct – Expansion is against zero external pressure.
(C) Incorrect – Free expansion is highly irreversible.
(D) Incorrect – Volume of gas changes, total volume available doubles, though system boundary is rigid. Final Answer:
\[ \boxed{(B) \; \text{Expansion of gas is not restrained by external force}} \]
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