# Work Done on a Gas Along Different Paths

## What is the work done on the gas along the paths AB, BC, CD, DA, and ABCDA?

Given that a gas following the PV trajectory of Figure 1 does 80 J of work per cycle, how can we calculate the work done on the gas along each path?

## Calculation of Work Done Along Different Paths:

To determine the work done on the gas along paths AB, BC, CD, DA, and the closed path ABCDA, we need to calculate the area enclosed by each path on the PV diagram.

When analyzing the work done on the gas along different paths in a PV diagram, it is essential to calculate the area under the curve for each specific path segment. By finding the area under the curve, we can determine the work done on the gas as it undergoes changes in pressure and volume.

**Path AB:** The work done on the gas along path AB can be determined by calculating the area under the curve between points A and B on the PV diagram using the formula W = ∫PdV, where P is the pressure and dV is the change in volume.

**Path BC:** Similarly, the work done along path BC can be calculated by finding the area under the curve between points B and C on the PV diagram.

**Path CD:** To determine the work done on the gas along path CD, we need to calculate the area under the curve between points C and D on the PV diagram.

**Path DA:** The work done along path DA can be found by calculating the area under the curve between points D and A on the PV diagram.

**Path ABCDA:** To find the total work done along the closed path ABCDA, we need to calculate the sum of the work done along each segment (AB, BC, CD, and DA). Add the individual areas under the curves for each segment to obtain the total work done on the gas along the path ABCDA.

For a more detailed explanation on calculating work done on a gas along different paths in a PV diagram, refer to the provided link.