An insulated chamber (allowing no heat to flow in or out) contains an ideal gas at a temperature T and volume V_i. That chamber is attached to an identical chamber via a small valve. The valve is opened, and some of the gas flows freely into the second chamber. There is nothing for it to push on, and no work is done. The gas is more dispersed, and its energy is more dispersed. Determine an equation for the associated change in entropy.