Question

The work done by an ideal gas during closed cycle \(1\rightarrow 2\rightarrow 3\rightarrow 4\rightarrow 1\) as shown in figure is

• A. \(P_{0}V_{0}\)
• B. \(2P_{0}V_{0}\)
• C. \(3P_{0}V_{0}\)
• D. \(4P_{0}V_{0}\)

Hint:

Work in a cycle is the area enclosed on the P-V diagram; when the loop crosses itself, subtract the area of the loop traversed in the opposite sense.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The net work done in a closed cycle equals the area enclosed by the loop on the P-V graph, taken with sign according to the direction of traversal.

Step 2: Calculation
Here the path crosses itself, so the cycle splits into two triangles traversed in opposite senses. The upper triangle is similar to the lower one with half the height. Taking the net area as the difference of the two triangles gives \(3P_{0}V_{0}\).

Step 3: Compare the options
The net work is therefore \(3P_{0}V_{0}\), which matches the third option.

Final Answer:
The work done in the cycle is \(3P_{0}V_{0}\). \[ \boxed{\text{(C) }3P_{0}V_{0}} \]