Question

A thermodynamic system is taken through cyclic process. The total work done in the process is:

• A. Zero
• B. 200J
• C. 100J
• D. 300J

Answer 1

The Correct Option is D

The total work done in a cyclic process is represented by the area enclosed by the graph in a PV diagram. The area can be calculated as the area of the rectangle formed by the points A, B, C, D, and E. The formula to find the work done is given by the area of the graph:

The change in pressure (height) is \( \Delta P = 400 \, \text{kPa} - 100 \, \text{kPa} = 300 \, \text{kPa} = 300 \times 10^3 \, \text{Pa} \).

The change in volume (width) is \( \Delta V = 4 \, \text{m}^3 - 2 \, \text{m}^3 = 2 \, \text{m}^3 \).

The area of a rectangle is \( \text{Area} = \text{height} \times \text{width} \).

Therefore, \( W = \Delta P \times \Delta V = (300 \times 10^3 \, \text{Pa}) \times (2 \, \text{m}^3) = 600 \times 10^3 \, \text{J} = 600 \, \text{kJ} \).

Corrected Calculation:

\(W = (400 - 100) \times 10^3 \, \text{Pa} \times (4 - 2) \, \text{m}^3\)

\(W = 300 \times 10^3 \, \text{Pa} \times 2 \, \text{m}^3\)

\(W = 600 \times 10^3 \, \text{J} = 600 \, \text{kJ}\)

Final Answer: The total work done is 600 kJ.