Step 1: Understand the process in a refrigerator.
In a refrigerator, the working substance (usually a gas) undergoes four main steps:
1. Absorption of heat from the refrigerated space.
2. Expansion of the gas, which cools it down further.
3. Heating of the vapor in the compressor, which turns it into a high-pressure gas.
4. Release of heat to the surroundings.
Step 2: Identify the correct sequence.
The correct order is first absorbing heat, then expanding the gas, heating the vapor, and finally releasing heat.
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 ____