In the Cyclic Process shown is the figure, the work done by...

In the Cyclic Process shown is the figure, the work done by the gas in one cycle
(A) $40 \mathrm{P}_{1} \mathrm{~V}_{1}$
(B) $20 \mathrm{P}_{1} \mathrm{~V}_{1}$
(C) $10 \mathrm{P}_{1} \mathrm{~V}_{1}$
(D) $5 \mathrm{P}_{1} \mathrm{~V}_{1}$

Key Concepts

Calculation of Work Using the Area Method

The area method involves calculating the work done in a thermodynamic process by determining the area enclosed by the process path on a P-V diagram. This method is particularly useful in cyclic processes, where the net work is equal to the area inside the closed loop, which can be computed geometrically or through integration depending on the complexity of the path.

Cyclic Process

A cyclic process is a thermodynamic process in which the system undergoes a series of changes and eventually returns to its initial state. In such cycles, state variables (such as pressure, volume, and temperature) revert to their original values, meaning that the change in internal energy over one complete cycle is zero, as per the first law of thermodynamics.

Pressure-Volume Diagram

A pressure-volume (P-V) diagram is a graphical representation of the changes in pressure and volume of a system during a thermodynamic process. Each point on the diagram corresponds to a unique state of the system, and the path taken during the process helps visualize how the system evolves over time.

Work Done by a Gas in a Cycle

In thermodynamics, the work done by a gas during a process is represented by the area under or enclosed by the process curve on the P-V diagram. For a cyclic process, the net work done over a full cycle is given by the area enclosed by the cycle, with the direction of traversal (clockwise or counterclockwise) indicating whether work is done by or on the system.

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