Thermodynamic Piston

A cylindrical chamber of cross sectional area \(\SI{4}{\centi\meter\squared}\) is filled with an ideal gas, and a piston of mass \(\SI{2}{\kilo\gram}\) sits at the midpoint of the cylinder. The rest of the chamber has total mass \(M.\)

Now, the piston is pulled very slowly upward. If the temperature of the gas inside the chamber remains constant, find the maximum value of \(M\) \((\)in \(\text{kg})\) such that the chamber can be lifted off the ground in this way. Submit your answer to 2 decimal places.

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Details and Assumptions:

• There is negligible friction in the system.
• Atmospheric pressure is \(10^5 \text{ N/m}^2,\) and \(g=10 \text{ m/s}^2.\)