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. 

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

The work done by a system during a cyclic process is represented by the area enclosed by the loop on a \(P\!-\!V\) diagram. Here, the cycle is a triangle \(ABC\).

To calculate the area of the triangle \(ABC\), use the formula for the area of a triangle:

\[\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}\]

In this diagram:

• Base (\(VC - VA\)) = \(5\, \text{m}^3 - 2\, \text{m}^3 = 3\, \text{m}^3\)
• Height (\(PB - PA\)) = \(300\, \text{Pa} - 100\, \text{Pa} = 200\, \text{Pa}\)

Substitute these values into the area formula:

\[\text{Area} = \frac{1}{2} \times 3\, \text{m}^3 \times 200\, \text{Pa} = 300\, \text{J}\]

The work done by the system in the cycle \(ABC\) is precisely \(300\, \text{J}\), which fits within the expected range of [300,300].