Someone has suggested that the device shown in figure below be used to improve the maximum force F against the spring, which has a spring constant of k. This is accomplished by changing the temperature of the liquid-vapor mixture in the container. You are to design such a device to close sun-blocking window-shutters that require a maximum force 0.5 Ibf. The piston must move 6 inches to close those shutters completely.

You elect to use R-134a as the working fluid and arrange the liquid-vapor mixture container such that the temperature changes from 70°F when shaded from the sun to 100°F when exposed to the full sun. Select the sizes of the various constant in this system to do this task. Also select the necessary spring constant and the amount of R- 134a to be used.