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 to 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 ______.