A thin-walled cylinder of mass m is filled with monatomic ideal gas and is lying on a horizontal frictionless surface. The initial internal energy of gas is U = cT. There is a thin insulating piston in the middle of the cylinder of mass M. The piston and the cylinder are heat-insulating and there is no friction between them. By a short impulse the cylinder is given a velocity v along its axis. Find the temperatures of the gases on different sides of piston when the piston stops oscillating.
The Attempt at a Solution
I am seriously lost. I was thinking about energy conservation, but since we have some external impulse acting on the cylinder and there is no way of measuring that we can't really write the conservation down I suppose. Also I don't see a thermodynamic approach to the gas processes? I do feel intuitively that the piston will not be in the middle of the cylinder when moving, but I can't really explain it, although possibly that might lead to the solution. Any hints appreciated!