A cylindrical vessel of length L, the side walls of which do not conduct heat, but the ends do, is sandwiched between thermal reservoirs with temperatures T1 and T2 (figure). Inside the vessel there is a thin piston that conducts heat, on both sides of which the vessel contains one mole of an ideal gas. Determine what position the piston will take after equilibrium is established. The thermal conductivity of the gas is assumed to be the same throughout the entire volume.

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