A horizontal cylinder is divided into two equal chambers by a frictionless, massless piston that is attached to an ideal spring (spring constant k) and can move without letting gas leak between the chambers. Both chambers contain the same monatomic ideal gas. Initially the left chamber is at 400K and the right chamber is at 300K; the spring is unstretched, and the entire cylinder is thermally insulated from the surroundings. Without doing external work, predict the direction in which the piston will move (left, right, or remain at the center) as the system evolves toward equilibrium, and briefly justify your answer in terms of entropy.