A thermodynamic process (B \(\rightarrow\) E) was completed as shown below. The work done is equal to area under the limits.
Step 1: In a thermodynamic process, the work done is represented by the area under the curve on the P-V diagram. From the given graph, the path \( B \rightarrow C \rightarrow D \rightarrow E \) correctly represents the work done in the system as the area under this curve.
Step 2: The other paths do not enclose the area under the curve in the correct manner to represent the work done during this thermodynamic process. Therefore, the correct path for the work done is \( B \rightarrow C \rightarrow D \rightarrow E \). Thus, the correct answer is option (3).
The left and right compartments of a thermally isolated container of length $L$ are separated by a thermally conducting, movable piston of area $A$. The left and right compartments are filled with $\frac{3}{2}$ and 1 moles of an ideal gas, respectively. In the left compartment the piston is attached by a spring with spring constant $k$ and natural length $\frac{2L}{5}$. In thermodynamic equilibrium, the piston is at a distance $\frac{L}{2}$ from the left and right edges of the container as shown in the figure. Under the above conditions, if the pressure in the right compartment is $P = \frac{kL}{A} \alpha$, then the value of $\alpha$ is ____