Question

A thermodynamic system is taken through the cyclic process \(ABC\) as shown in the \(P\!-\!V\) diagram. The total work done by the system during the cycle \(ABC\) is _______ J. \includegraphics[width=0.5\linewidth]{50.png} Given: The area enclosed by the cycle in the \(P\!-\!V\) diagram represents the work done.

Hint:

In cyclic thermodynamic processes, work done is always equal to the area enclosed by the cycle in the \(P\!-\!V\) diagram.

Answer 1

Correct Answer: 300

Concept: For a cyclic process: \[ W=\text{Area enclosed in the }P\!-\!V\text{ diagram} \] From the diagram, the cycle forms a triangle.
Step 1: Identify base and height \[ \text{Base } = (5-2)=3\,\text{m}^3 \] \[ \text{Height } = (300-100)=200\,\text{Pa} \]
Step 2: Calculate work done \[ W=\frac{1}{2}\times\text{base}\times\text{height} =\frac{1}{2}\times3\times200 =300\,\text{J} \] Final Answer: \[ \boxed{300\ \text{J}} \]