Question

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?

• A. Work done is equal to the area under the curve of a \( p-V \) diagram
• B. Expansion of gas is not restrained by external force
• C. The entire process is reversible
• D. The overall change in volume is zero for the entire system

Hint:

In free expansion processes, no work is done by the gas because there is no external pressure. The process is spontaneous and irreversible.

Answer 1

The Correct Option is B

When the partition is removed, the gas expands into the previously evacuated compartment. This is a typical example of a free expansion process where the gas is not subjected to any external pressure. In this process, the gas occupies the entire available space, and no external forces act against the expansion of the gas. Therefore, the expansion is unrestrained by any external force.
Option (A): This option is incorrect because the work done by the gas in a free expansion process is zero. The expansion occurs without any opposing external pressure, so there is no area under the \( p-V \) curve to represent the work done.
Option (B): This is the correct answer. In free expansion, the gas is not opposed by any external forces, and hence it expands freely to occupy the available volume.
Option (C): This option is incorrect. The process of free expansion is irreversible. Once the gas has expanded into the second compartment, the process cannot be reversed without additional work or constraints.
Option (D): The change in volume for the entire system is not zero. The gas expands into the second compartment, increasing the overall volume of the system.
Thus, the correct statement is (B) Expansion of gas is not restrained by external force.