An insulated container of mass M and length L is at rest on a horizontal frictionless surface. The container is filled with an ideal gas of unknown mass m and temperature T. The container is divided in half by a light movable insulated piston.

A heater is turned on inside the left part of the container, bringing the temperature of the gas there to 2T. The temperature of the gas inside the right part of the container remains unchanged. As a result, the container moves a distance x along the surface. Find the mass of the gas m.

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