Question

An ideal monatomic gas follows the ABCDA path in the adjoining P-V diagram. The work done by the gas will be

• A. \( \frac{1}{2} PV \)
• B. \( PV \)
• C. \( 2 PV \)
• D. \( 4 PV \)

Hint:

In cyclic processes, the work done by the gas is the area enclosed by the path in the P-V diagram.

Answer 1

The Correct Option is B

Step 1: Understand the path of the gas in the P-V diagram.
The gas undergoes a cyclic process represented by the ABCDA path in the P-V diagram. In such a cycle, the work done is equal to the area enclosed by the path.
Step 2: Calculate the work done.
For the
given path, the area enclosed by the rectangle formed in the P-V diagram corresponds to the work done. The work done \( W \) is:
\[ W = P \times V \] where \( P \) and \( V \) are the pressure and volume at the initial state.
Step 3: Conclusion.
Thus, the work done by the gas is \( PV \).
Conclusion:
The correct answer is (B) \( PV \).