I have three vessels shown in the figure. The ground area of each vessel is A. The vessels are in diathermic contact with each other by the disk on which they are mounted. Each vessel is closed by a piston that is mounted to the long arm with a distance from the center of the long arm shown in the figure. Last there is no external pressure acting on the vessels. I should calculate the ratio of the pressures and the temperatures inside the vessels.
What I would do now is to assume some angle $\alpha$ representing the angle of the envelope of the long arm to which the pistons are mounted. The next thing I would do is to assume that the distances from the pistons to the long arm are constant and out of this I would compute the accessible volumes of the vessels what would tell me the pressure ratios and temperature ratios. But my feeling tells me that this is wrong. Can anybody give me a hint a to consider this problem or how to start??