One mole of ideal gas is in a vessel between two massive pistons connected by a light thin inextensible thread. The pistons can move without friction along the axis of the vessel, there is no external pressure. The area of the upper piston is 500 cm ^ 2, the area of the lower piston is 300 cm ^ 2. It is known that the maximum temperature at which such a system may exist is 350 K. Find the minimum temperature at which such a system may exist.

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