Question

Find work done by gas in cyclic process:

• A. \(100\,\text{J}\)
• B. \(-100\,\text{J}\)
• C. \(200\,\text{J}\)
• D. \(-200\,\text{J}\)

Hint:

Always check the {direction of the loop} in a \(P\!-\!V\) diagram: anticlockwise loops mean work is done {on} the gas.

Answer 1

The Correct Option is B

Concept:
In a cyclic process
, the net work done by the gas is equal to the area enclosed
by the loop on the \(P\!-\!V\) diagram.

Clockwise cycle \(\Rightarrow\) positive work
Anticlockwise cycle \(\Rightarrow\) negative work

Step 1: Identify the Cycle Direction
The process follows the path: \[ A \rightarrow B \rightarrow C \rightarrow A \] which is an anticlockwise
cycle. Hence, work done by the gas will be negative
.
Step 2: Calculate Area Enclosed
The cycle encloses a triangular area. Base: \[ \Delta V = 4 - 2 = 2\,\text{m}^3 \] Height: \[ \Delta P = 300 - 200 = 100\,\text{N/m}^2 \] Area of triangle: \[ \text{Area} = \frac{1}{2} \times \Delta V \times \Delta P = \frac{1}{2} \times 2 \times 100 = 100\,\text{J} \]
Step 3: Assign Sign
Since the cycle is anticlockwise: \[ W = -100\,\text{J} \] \[ \boxed{W = -100\,\text{J}} \]