Question

A gas is taken through the cycle A B C A, as shown. What is the net work done by the gas?

A. $3000J$
B. $1000J$
C. Zero
D. $2000J$

Answer 1

A cyclic process is defined as one in which the initial and final states are the same. It is a series of events that end with the system in the same state as when it began. As a result, in a cyclic transition, the work done by the system equals the heat absorbed by the system.

Complete step by step answer:
The area contained by the curve of a cyclic process represents the total work done in that process. Positive cycle or work producing cycle, i.e. work done by the system, is shown by the clockwise orientation of the cycle curve. Negative cycle or work absorbing cycle, i.e. work done on the system, is shown by the anticlockwise direction of the cycle curve.

Work done in a cyclic process equals the area under the cycle, which is positive if the cycle rotates clockwise and negative if it rotates anticlockwise.

W = Area of the cycle ABCA is the net work done by the gas.
$\Rightarrow W = \dfrac{1}{2} \times BC \times AC \\\ \Rightarrow W = \dfrac{1}{2} \times \left( {7 - 2} \right) \times {10^{ - 3}} \times \left( {6 - 2} \right) \times {10^5} \\\ \Rightarrow W = \dfrac{1}{2} = 5 \times {10^{ - 3}} \times 4 \times {10^5} \\\ \therefore W = 10 \times {10^2}J = 1000J$
Therefore, the net work done by the gas is $1000J$

Hence, the correct option is B.

Note: Cyclic processes are those in which a system goes through a series of processes before returning to the same condition from which it started, completing a cycle.The system does not go back to the beginning of its journey. The reversibility or irreversibility of a cyclic process can be determined. If all of the processes that make up a cyclic process are reversible individually, it can be deemed reversible.