Heat and Thermodynamics

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 ‌

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 ‌

2L

5

In thermodynamic equilibrium, the piston is at a distance ‌

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=‌

kL

A

α, then the value of α is ____