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 \( \dfrac{3}{2} \) 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 \( \dfrac{2L}{5} \). In thermodynamic equilibrium, the piston is at a distance \( \dfrac{L}{2} \) 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 \( P = \dfrac{kL}{A}\alpha \), then the value of \( \alpha \) is ____.
