An ideal gas is taken around a closed cycle ABCA as shown in the p-V diagram below. The coordinates of the points are: A(V, p); B(3V, 4p); C(3V, p). What is the work done during one complete cycle?

Correct option is D

The correct answer is (d) 3pV

Explanation:

In a p–V diagram, the work done during a closed cycle is equal to the area enclosed by the cycle.

The given cycle ABCA forms a right-angled triangle with vertices:

• A (V, p)

• B (3V, 4p)

• C (3V, p)

Step-by-step:

• The base of the triangle (horizontal distance) is:
  Base = 3V − V = 2V

• The height of the triangle (vertical distance) is:
  Height = 4p − p = 3p

• Area of triangle (Work done) = 1/2 × Base × Height
  = 1/2 × (2V) × (3p)
  = 3pV

Therefore, the net work done in the cycle = 3pV.

Information Booster:

• If the cycle is clockwise, the net work done is positive.

• If the cycle is anticlockwise, the net work done is negative.

• Work done is a path function, meaning it depends on the specific process followed, not just the initial and final states.

Additional Knowledge:

pV (Option a) would be correct only if the base was V and the height was 2p, which is not the case here.

So, the correct answer is (d) 3pV.